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.
