Mr. Paik may have actually intended the watch to end up on the island, sending Jin and Sun purposely on the flight.
One of Paik's men warned Jin not to run away at the airport. So it was not intended
Jin was supposed to fly to LA (where 815 was heading) to give the watch to somebody. Paik's man told him not to run away, not to not get on the plane. So it's still possible that Paik purposely sent Jin and Sun, with the watch, to the Island.
The watch may serve a specific purpose in unlocking one of the keys of the island, such as containing something within it that activates the giant magnet within the station.
The watch may have been intended for someone at Widmore Labs, as it supposedly has locations in California, and is associated with Paik Heavy Industries, which is the same name as Mr. Paik, and the man in the Hawaiian Shirt told Jin the watch was intended for Paik's friend in California.
The pair of Rolex watches might contain some sort of transponder, allowing them to communicate with each other or transmit GPS coordinates to the outside world. Paik might have known that Jin and Sun were about to be transported to a secret DHARMA facility, but he didn't know its location. He might have given Jin the watch (with a GPS tracker embedded in it) as a safeguard to find his daughter, or to discover the location of the facility (the island).
He wanted to use the island's top secret coordinates as leverage when bargaining with The Hanso Foundation for more contracts.
Jin's handing over of the watch was to be a signal for whoever he gave it to, to kill him.
In season four, if Michael returns to the series, this device will be ideal in connecting Michael to any employee of Mr. Paik, as it can tell a Paik associate that Michael has recently been in contact with Jin & Sun. This can be used for dramatic purposes in a variety of ways, but Michael will probably get beat up again due to misunderstanding.
Is the same as Jack's watch in the mobisode.
Because Michael pawned Jin's old watch, and since the watch is of huge importance that Jin had to deliver it to the states, this is now a piece of evidence to the outside world that their are survivors of flight 815. Someone familiar with Korean and Korean power players reads the back of the watch, realize that it is from Sun's very wealthy and powerful father, and the watch gets back to him. With the watch's existence in the outside world, he will realize that his daughter and son-in-law are still alive, go try to find them, and eventually find out about the island. Maybe he disrupts Widmore's work or Ben's work or both, but Michael selling the watch for the gun is potentially very important.