Continuity mistake: As they are fleeing the alien base, Supergirl and the others run towards the portal, Winn activates it and jumps through. In a following shot (after a 'friendly' alien helps them), he is standing behind Supergirl again. (00:32:00 - 00:32:35)
Continuity mistake: When the alarm in the office goes off, there are clocks visible around the alarm. The time on the New York clock is 10:40. About 15 seconds later, as the agents go into the meeting room, the New York clock has gone back 5 minutes to 10:35. It is definitely the same clock because the alarm is visible next to it. (00:03:40)
Let Sleeping Zords Lie - S1-E7
Continuity mistake: Kendall is wearing black heeled boots when she is fighting the aliens, switches to black sneakers when she lands after being thrown and has the boots again when she stands back up.
The Marriage of Lupin III - S1-E1
Continuity mistake: Right after his old pals left Lupin alone at the wedding reception, Rebecca jumps at him from behind. She places both hands on his shoulders, but in the next shot she has just her left hand on his matching shoulder. (00:05:35)
The Incubus - S1-E9
Continuity mistake: In episode 5, it was established that there is no road to the Jezequiel house. Robert and Max had to leave their car in the village and walk across the fields to the house. In this episode, however, Robert drives his car right up to the house with no problem.
Continuity mistake: The quantity of super-steroid in Fukegao (the mad scientist) 's test tube changes continuously between shots. (00:11:00)