Captain Gault is the man who is/was engaged to Penelope.
Captain Gault is a captain of a freighter, not the man Widmore would found worthy.
The unsurprised look on his face as Sayid reveals Michael's treachery is due to Gault already knowing Michael's real story.
Gault is possibly a "double agent" working for both Widmore and Penelope, who has no intention in harming the 815ers - maybe he supported Michael in his efforts to sabotage the ship or at least didn't punish him because he knew who Michael really was. In this case "don't trust the Captain" could have been written by someone entirely else than Michael, as everyone expected, for example Lapidus.
Captain Gault's name could be a reference John Galt, a character in Ayn Rand's novel Atlas Shrugged, who leads a strike which stops the self-destruction of the world's economy.