Members Only - S1-E2
Continuity mistake: In the last scene, when Daffy and Bugs are talking to each other, Daffy's towel is yellow and in the next shot, it's white.
The Muh-Muh-Muh-Murder - S1-E25
Plot hole: Daffy isn't able to escape Porky's house until he gets the keys, but later it is revealed that the reason he couldn't get out was because he was too weak to open the door. If that was the case, the keys shouldn't have been able to help him get out.
Continuity mistake: When Sylvester enters his mother's house, he slides the glass door from the wall to the middle and right to left (from viewer's perspective). But when he closes it, he closes it from right to left so it closes in the middle, even though it wasn't set up that way.
Continuity mistake: When Granny tells Sylvester to stop chasing Tweety Bird, he comes to a stop and Tweety Bird keeps going and is ahead of him. But in the next shot, Tweety is now behind Sylvester (between Sylvester and Granny), however, there's not enough time for him to fly back that far (or even circle around), and we would have seen him do it.