Trivia: This is for the trailer rather than for the final film, but worth a look. At 1:33 in the trailer, just after seeing Rorschach slam someone against a wall, we see another fight. Pause it and look at the guy in black - he's holding a walkie-talkie, which in the next shot becomes a gun. This is only trivia, not a mistake, because it's only valid for the trailer. The MPAA don't allow guns to be pointed at the screen in trailers, so Zack Snyder, in a tribute to the infamous gun-editing from E.T., replaced the gun in that one shot with a walkie-talkie.
Continuity mistake: When Dan returns home after talking to Mason, he finds Rorschach in his kitchen eating beans from a can. After he has finished eating, he throws the second can on the table where it lands next to another can. When he gets up, the two cans have moved significantly apart.