Corrected entry: In order to find out where Jack is, Marvin calls up the credit card company to find out where Jack last used his card. How did Marvin know the company he called would be the company that Jack has a card with?
Corrected entry: There is no way Agent Mosely could not know that he didn't have his identification, he would need it to get in and out of FBI headquarters as well as it being standard procedure to show his identification when announcing that he is an agent.
Correction: Mosely never reaches for it when he meets the pilot. It's possible he knew it was missing off screen and figured he just misplaced it. Only after the pilot tells him that Walsh used his name does he and the other agent figure out where it really went.
Correction: He has the card number - of course he knows which card Jack has. It is clear from the script that the two men know everything there is to know about the other.