This place is somewhere in the high mountains. Possible reason for this is to increase the range of the direct visibility of some sensor devices.
The location is in the "zone of interest" claimed by Portuguese-speaking Brazil extending from 60°S to the South Pole and from 28°W to 53°W known as Antártica Brasileira.Map
The station is located near the Antarctic Peninsula - near Brazil's only permanent research station on the ice -- Estação Antárctica Comandante Ferraz (EACF).
The location is in the Himalayas, as there appeared to be soft Indian (Sitar) music playing in the background.
There is a clue to strenghten this : Nepal's name in Pali language is... Na-pali. Pali meaning something like "straight vertical line" and being the liturgic tongue of Buddhism. This name probably refers to the high cliffs you find in the Himalayas, but also found on the island. And there is a place in Hawaïi that looks strikingly similar to the filming location : the Na-Pali coast. 
It is located in Iceland, maybe near the Vik Institute. It's south of the arctic circle, so there's no problem with it being
It is a nuclear submarine in Antarctica, maybe left over from the Cold War.
It is located in Vladivostok, Russia, and is the same one that Mikhail used to work in. The discharge took place in late November, when snow is quite common in Vladivostok.
The exact location doesn't matter, as long as it's well isolated from man-made and natural electromagnetic sources that could mask the very weak signal they are trying to detect. Since the Island is in the southern hemisphere, that's probably where the monitoring station(s) are also.
The station is located somewhere near Camp Millar. Theory based on a clue found on FIND 815.
The Portuguese-speaking men are near the South Pole. While the North Pole tends to collect most of the electrically charged particles flowing around the earth (and would thus make for a perfect spot to monitor the earth's magnetic field and electrical/ionic behavior), this episode takes place during November (September 22 plus 65 days), a time when the Arctic experiences darkness all day. The last scene of this episode, however, starts with an establishing shot of a snowstorm seen by daylight. It is also possible that the Portuguese-speaking men are on a high-altitude location, and/or on the northern hemisphere south of the Arctic Circle.
The station is run by the "bad guys" tying to find the Island.
owned by DHARMA, in relation to Penny, who also works for DHARMA. The station is in Antarctica, and we find out that Penny's 'chance' meeting with Desmond at the monastery was set-up. This is made a bit more tangible by the tenuous relationship between Widmore Corporations and Hanso/DHARMA. See also Naomi/Theories.
The station is some sort of magnetometer. They monitor magnetospheric activity. Magnetometers are capable of measuring geomagnetic pulsations, (ULF [ultra low frequency] magnetohydrodynamic waves), in the Earth’s magnetosphere.
The station isn't tracking electromagnetic anomalies, but actually trying to track the boat (perhaps given to Desmond by Penelope, via Libby, who was hired for that purpose). The Island's electromagnetic field normally makes it impossible to track the signal from a boat. However, whenever the button isn't pressed, the reaction that occurs somehow makes it possible for the boat's signal to escape and be picked up by the outside world. This occurred once before, when our survivors' plane was brought down; apparently the pair at the listening post weren't able to secure the signal before the surge was over. This time, they got it.
The text "1bbybby" that appears on the computer screen is a code or corruption of the word "Libby". Therefore the men may have been keeping watch for Libby, not Desmond.
The station is actually receiving the transmission from the radio tower on The Island as discussed in the Sri Lanka Video (The Lost Experience). The alert is because one of the numbers being broadcasted has been changed. When Penelope is told "We found it", they mean that they have found a way to change the one of the numbers.
So they just randomly appeared close to the Island? They were in fact talking about the fact that they found the Island.
The radio tower has already stopped broadcasting the numbers, as Danielle Rousseau has changed it to her message.
As previously noted, the phone has no numbers on it but Henrik's first action is to turn to the page in the black binder labeled "Emergency Numbers". Not to mention he gave Mathias no other instructions, no certain person to call he simply yelled, "make the call!"
The Emergency Numbers aren't contact numbers, otherwise it would have said that; they're the numbers he is to type into his computer in order to reset the fail-safe device and return The Island to its normal state (e.g. the computer in the listening post is connected to The Island).
Alternatively, it's a list of numbers that can represent electromagnetic variances, i.e. 7418880
It isn´t a non-sense number: 4*8*15*16*23*42= 7418880
Like Penelope Widmore stated in "Live Together, Die Alone, Part 1", she has a lot of money, so she bribed the workers at the station to contact her if the system ever failed again and that’s why the yellow phone cord was strung across the entire floor because it wasn’t a normal part of the building. (The writers made a point of showing us this since Mathias tripped over the cord.)
It's also why Mathias said "We missed it again; they will kill us." They missed the last System Failure and the only reason they're not already dead is because Desmond reset the countdown just in time.
If the station exists to attempt to locate the Island (or the sailboat), then there are probably multiple stations. One station cannot determine the location of a signal source, but multiple listeners can use triangulation to pinpoint the source.
Perhaps the reason Desmond was drawn to the Island was because the system nearly failed. Then when Desmond failed to turn up at the end of the boat race, Penelope Widmore when looking for him and any possible reason for him to have gone missing, she then learned of a strong magnetic outburst that happened during the race. She then set up the listening station to find the magnetic outburst, The signal they missed was the one that caused flight 815 to crash.
So? There could have been other system failures that have happened in the past.
When the scene occurred
This scene was actually Lost's first flash-forward. While presented as occurring straight after the sky turned purple, it actually occurred moments before Penny picked up the phone to Charlie, about a month later. The flashing text on the monitor was an incoming phone signal. The sky turning purple merely prompted Penny to buy/build the station in the first place as she found this out some other way.
Or perhaps it occurs even later than that. The Oceanic 6 plus Desmond ask Penny to use her listening station to find the Island for them so they can return to it. We'll see an extended version of this same scene in a future season that will reveal Desmond in the bed next to Penny after she receives this phone call.
Story wise, this could make sense, but the Enhanced episode of "Through the Looking Glass" states that Jack's bearded flash forward is the first "flash forward" of the series. Penny was also jarred out of bed by the phone call from the station, and in Charlie's receiving of Penny's call, I believe she was in some kind of office environment.
There is no evidence for this, why even suggest it.
Next to the terminal is a small stack of letters that don't appear to have an address on them but they DO have a return address - a close-up of the terminal image suggests the name on the return address is "Desmond Hume". (image)
Even the address, when compared to Desmond's letters, is extremely similar in length and form.
The missed anomaly may be the same event that brought down Flight 815.
The missed anomaly may be related to Locke's failure to push the button before the timer expired in One of Them.
It's unlikely. It's strongly suggested that the Toomey listening station is in Australia.
Their station was in the Pacific I believe, but it is more likely to be the listening post where Mikhail was stationed.
IP addresses in the network range 10.0.0.0 to 10.255.255.255 are reserved for private networks. This means the station is somehow networked to other stations or locations using a private network, probably somehow related to the Widmore empire. Possibly, other locations have alerted this station of the anomaly, or might have been updated of the anomaly by this station.
Many scientific instruments these days are connected to PCs via a LAN. The messages are probably from an instrument array within the listening post itself.
Seeing as how the maximum distance of an ethernet connection is 2500 meters, then the people they were talking to have to be 'close.' The reason why this is so is because with it being a private (non-routeable) address, then there is a 'private network,' meaning they are connected to each other, and not necessarily to the outside world.
This assumes there is a direct point to point connection between "there" and the station. Whist not usually done there is no reason why a very long connection cannot be made (over 2500m stated above) by adding in more complex network devices than simple ethernet repeaters which the 2500m rule is based on. It would effectively mean a "private internet" and probably not viable from a finance point of view, but it is possible.
It could be on the Internet but behind a NAT router, like the majority of home-broadband-sharing routers on the market.
None of the assumptions being made are right. The mostly likely connection between the station and the outside world is a sat link of some kind. The station is likely in Antartica and there is no physical cable connectivity in the first place. If you have your own channel on the sat, you can make the IP addresses on either end whatever you like. A large company like Widmore would not send sensative private data from a research station across the public internet. They would own enough infrastructure to keep the traffic and the addresses private.
Being seven digits long, it might be a phone number sans-area code (likely in North America, perhaps part of a toll-free number).
The conversation between the men is understandable, but the accent is quite heavy. There are two plausible theories for the heavy accent:
It is simply a production glitch. The characters are supposed to be native Portuguese speakers, but the producers of Lost could not or would not cast native Portuguese-speaking actors. Another example of this is the clumsy, heavily accented Arabic used in the episodes involving Sayid flashbacks. If so, then it's irrelevant.
Actually, they were originally supposed to be Russian, but they found two actors that happened to both speak Portugese so they went with that. Their accents/language are completely meaningless.
The characters use Portuguese as their "lingua franca." They cannot speak each other's native tongue and thus use Portuguese as a middle ground. (Portuguese is not commonly employed as a lingua franca, so this would mean that the characters, although not having Portuguese as their mother tongue, have both lived in a Portuguese speaking environment and have learned the language.)
The Listening Station is similar to the hatch, because it is a secluded station with people who may or may not know what their mission is exactly, but still perform their duties, similar to pushing the button. There are two people, the same amount of people "recommended" for the hatch.