After Ward has already set up the trap Wally asks if he can set it up. Then when he picks up the stick to do so there's no longer a string tied on it.
When they set up the trap there's 2 holes on the side of the box but when they catch the rabbit there's only 1.
A door has suddenly appeared across the hall from the boys' room, to their parents' room. In earlier shots of outside the boys' room, there was no door across from theirs.
It may not have been generally known in 1958, but it's an urban legend that rabbits reject (or kill) their kits, or babies, if they're handled by humans. It's more likely that a female rabbit, or doe, will bite a human who tries to pick up her newborn young. Does do sometimes attack their kits after the birth of their first litter, but this is usually the result of trauma or injury, not handling.
Beaver tells Larry that maybe he can have one of the rabbits after their eyes open but they are shown with their eyes already opened. (especially when Beaver is holding one)