Continuity mistake: When Robin leaves to get Battleship, Barney thinks they're going to have sex, whips his belt off, and throws it on the floor. When Robin returns, he's neatly folding his pants and draping them over a chair, and his belt is still threaded through the loops. (00:16:20)
Suggested correction: He could have easily done that himself so it was easier to put back on afterwards.
This correction is too much of a stretch. It would make no sense for him to take off the belt and throw it to the ground in the first place. He was alone at that point, so he wasn't doing it to impress anyone and he's been in this position before.
Continuity mistake: When Robin and Barney meet up for drinks, the amount of ash on the end of Barney's cigar goes up and down frequently between shots. (00:06:10)
Continuity mistake: When Barney is pointing out the woman in the blue shirt at the bar, Robin's drink changes from one hand to the other to the bar between shots.