After Dr. Horrible is beaten at the bridge dedication, he blogs with a bloody left eye and a bruise below it. When he visits Penny at the laundromat, he has no injuries.
During the song "Brand New Day" Dr. Horrible jams all of the darts into the center of Captain Hammer's face on the board. In the next shot, we see the darts all over the board, despite him walking from the board to the couch.
When Moist and Dr. Horrible are discussing about killing someone to get into the Evil League of Evil, the shadow of the boom mic can be seen on the wall behind the doctor near the ceiling. Right when Dr. Horrible states that he won't kill a little kid the mic shadow is seen moving towards him.
Dr. Horrible implies that he lives in Los Angeles, by stating that the L.A.P.D. are among the viewers of his blog, but in the flashback of Captain Hammer beating up Dr. Horrible, there is a scene with snow on the ground, and large snowflakes in the air. Los Angeles has very mild winters, never getting below freezing during the daytime, which is when the fight took place.