The Adventures of Supergirl - S2-E1
Continuity mistake: When Kara saves the chopper the sun on the floor changes between shots.
Continuity mistake: When J'onn J'onzz is fighting Miss Martian in the ring, she punches him into a wall, leaving a massive dent. She missed the next punch, and the plaster on the right hand side of the dent falls out, but the plaster on the left is fine. Miss Martian then throws J'onn across the room, and in the background, the dent is visible, but it is now the left hand side of the dent where the plastering is missing and the plastering on the right is now mostly in place.
Continuity mistake: Mike and Kara are in the alien bar in the both talking about Mike not controlling his powers. When Mike breaks the glass there is no other glass on the table. In the next shot a glass appears at the edge of the table, in the next shot the glass is gone again. (00:03:30)
Continuity mistake: Maggie comes to Alex's apartment with pizza. When Alex opens and closes the pizza box, she folds the pizza box edges in and 3 shots later the edges are outside of the box.
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)
Homecoming - S2-E14
Continuity mistake: In the scene at the end where Mon-El goes to Kara's to try and console her, right after he sits down and she shifts to lean on him the blanket falls off her shoulder, but in the next shot it's covering her once again. (00:40:35)
Continuity mistake: Rick Malverne has handcuffs on when J'onn goes in as his dad. When he figures out it was J'onn, he tells them they have "23 hours and 14 minutes," looks at his watch and the cuffs are gone. (00:21:30 - 00:25:00)
Continuity mistake: Right after Alex is freed from the water tank, in the shots of Maggie holding her, Alex's clothes are bone dry.
Answer: Another part of why the change was that it's cold in Canada in the winter and the old costume didn't protect her from it, whereas the new one is nice and warm.