Continuity mistake: In the Season 1 episode "Bollo", Bob Fossil records Howard saying "Gorilla" on his talk box, which Howard does with a downward inflection at the end of the word. However, every time Fossil plays back Howard's "Gorilla", it has an upwards inflection at the end of the word.
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: At the diner when Tsunoda and Retsuko are talking, Tsunoda pulls out a red phone with a white heart on it from her purse. In the close up she is pulling it out with her left hand and the phone is horizontal with the heart on its side. It then cuts to a wide angle and suddenly she's holding the phone upright with both hands.