Revealing mistake: During "A Man's Gotta Do", when Captain Hammer kneels down and crushes the gizmo on top of the van, you can briefly catch a glimpse of a black safety cable next to his knee.
Continuity mistake: When Moist asks Dr. Horrible if he needs anything "dampened or made soggy?", the expression on his face changes instantly between cuts.
Other mistake: During "My Freeze Ray", there's a shot where Billy, Penny, and several other people open doors to the laundry machines in sequence. When Billy opens the door to his machine, you can see the reflection of everyone else just standing there, waiting for their cue to walk forward.
Continuity mistake: During the very beginning of "My Freeze Ray", as Dr. Horrible is about to set down his basket of laundry, the bottle of detergent sitting on top of his clothing rotates 90 degrees after the scene briefly cuts to Penny.
Revealing mistake: During "Brand New Day", watch the background as Dr. Horrible appears as a giant and stomps down the city-street. As he takes his first step, a piece of concrete from building to his right falls off and hits the ground. However, if you look closely, it's obviously a quickly-made computer effect. As the piece of concrete hits the ground, it simply vanishes, and is replaced by a rather odd-looking animated "poof" of dust. The issue is the concrete piece was much bigger than the cloud of dust, so it's clear that the piece simply disappears right as the dust-poof appears.
Continuity mistake: During "Brand New Day", at one point, Dr. Horrible stabs a picture of Captain Hammer attached to a dartboard with a handful of darts, all right in the center of the picture. A few shots later as Dr. Horrible sits, suddenly the darts are far-more spread out. (It's in the background and can be hard to see, but it's noticeable.)