When Mal and Chippie first enter the loan company (the front for Walters' bookmaking organization), the signs on the windows both say "Libert Finance" - both "Libert"s clearly have a last letter - a "Y" - painted over. Eight minutes later in the film, when L.A.'s new "Gangster Squad" is going over a file about the company, both signs in a photo say "Libertt Finance" (with a "T" replacing the blacked out "Y" seen earlier).
At Boulder (Hoover) Dam, Granger and Gail are in the very front of a packed elevator descending into the dam. But when the elevator reaches the bottom, several people get out before they do, which should not happen given how crowded the elevator was.
The tape recorders Mal uses to manipulate the Vegas sports book only have one reel. But this isn't a goof because he is recording announcements from the race track on one tape deck (with only a feed reel) and playing the tape back to the bookie network after a 2-minute delay on the second tape deck (with only a take-up reel. If you look closely at the shot, at some point you can see a big pile of loose tape from in between the reels sitting on the table in the background -- which is probably about 2 minutes worth of tape. That's how he gets the delay.
Just past the one hour mark, the camera crew is reflected in the side of a car.