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.)
Continuity mistake: When Moist asks Dr. Horrible if he needs anything "dampened or made soggy?", the expression on his face changes instantly between cuts.
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.