The Ajira Airways will be a flight from Los Angeles to a Middle Eastern or Asian city. This plane, as was the fate of Oceanic 815, will 'disappear' and become the source of another conspiracy, possibly the final move that causes the whole conspiracy to be discovered. This will be the vessel that takes Jack, and co. back to the Island and will be a device by which new characters are introduced to the Island.
The Ajira Airways is the end of the planned ARG. It is the punch line - the thing that will have the most relevance to the show. They can cut the middle of the ARG, but this part needs to be included for some reason related to the show. It is the season 4 equivalent of the underwater airplane discovery in Find 815.
Ajira Airways is a wholly-owned subsidiary of Mittelos.
Relatively few questions were shown being asked of any of the passengers upon boarding. Jack was asked several question regarding Locke's casket but nothing else. It is definitely possible that we just were not shown the questions.
Kate is breaking her probation and showing her identification should hit some "no-fly" database. The "no-fly" database in the non-fictional world consists of terrorists and other threats to national security; it does not consist of the name of every one on probation, but in this case there has to be something that should have prevented Kate from flying that did not do its job.
Kate had spent years running from the law prior to the Island. It would be old hat for her to get fake identification.
Ben was visibly injured and when he walked onto the plane. No one displayed any interest in ensuring the comfort of an injured first class passenger.
Frank Lapidus happened to have been hired by Ajira and happened to be the pilot of Flight 316. That is a very convenient pair of coincidences.
No one displayed any recognition of any of the Oceanic Six. The media are fickle. If it did not happen yesterday...; that is overly cruel, but the media do make their money by reporting current events and they would have to have stringers, who might be airline employees, watching for "watchable/readable news." It is 2008. Hurley was recently recognized by a store clerk, but he was cleared of any wrongdoing and released. Sayid is in custody. He and Sun are both foreign faces in a crowd.
Juliet immediately recognized their logo on the Ajira water bottle. She used to be a doctor in Miami; Ajira flies over the Pacific. She knew about Ajira because its being controlled by the Others/Mittelos was common knowledge.
The Ajira employees were actually Others or non-Others tasked to do what Mittelos orders.