Revealing mistake: When Tony is having his first fight in the embassy, it is obvious that most of his punches do not connect at all. The people he supposedly hit still react as though being hit, and the sound effects of a fist hitting a jaw are still there, even if Tony misses by several inches.
Revealing mistake: When Puma Man picks up a gangster and flies him over the construction site, he drops the man to intimidate him. The gangster does not fall straight down, but slides downward at an approximately 45 degree angle to the ground. Either the actor was attached to a wire, or someone flipped the background shot, or a combination of the two. Either way, the downward "fall" looks completely wrong.