Archer, after giving instructions to the team (and draining his flask), says he's going to go up to the executive offices to find an override code for the vault. Pam adds, "and also find more booze that you just ran out of." Archer replies, "You know, I was being nice before, Pam; your skin doesn't look that much better." However, it was Ray, not Archer, who earlier had said to Pam, "... your skin has been glowing lately." as the ending to his "compliment sandwich".
The written document Fabian hands Cyril to confirm ownership of the agency that will be returned after they do the bank heist, of course, cannot be legally enforced, because the condition is that they commit a crime. It is, therefore, useless, and Cyril would know that.
It is portrayed that Fabian employed verbal trickery to appear to offer something better than what he'd actually deliver. One aspect is paying their budget for 6 months. The trick is that he backdated it to the *last* 6 months (which he was already paying anyway). However, he literally said "Next 6 months". This is an out-and-out lie, not verbal trickery.
Lana, locked in a vault, reveals that an important phone call was cut off and, thus, searches for reception. Once she finds it and returns her call, she changes position and starts walking around and loses the call again, despite already being fully aware that almost the entire vault is a dead zone, and she should know she can't move.