When the bucket of pink paint falls on the man's head, his upper body becomes completely covered in pink, yet a moment later as he continues to chase Pinky out of the house with the shotgun, his upper body is clean and white again.
Two instances of inconsistency as the painter is blasting away at Pinky with the paint-filled shotgun; in both cases, a paint-splashed portion of the outside wall of the house does not correspond between close-up and wide-angle shots: the left front window is sprayed and then it is clean in the wide-angle shot (only the wall below the window is sprayed with the pink paint instead of the window, also), and then the upper right-hand corner of the roof is not sprayed in the wide-angle shot but then is shown to be painted in a close-up when Pinky points out the remaining "unpinked" blue-painted spot to the painter.
When the panther is painting one wall and, not quite done, camouflages himself in the paint to hide from the little man, the words "WET PAINT" miraculously appear in the white part of the wall on the next shot of it.
The painter's jumbo-sized mouse-trap gets tripped when Pinky pulls the tape measure's rule out and then lets it zip back in, yet when the painter trudges dejectedly across the frame again a moment later with the tripped trap clamped onto his posterior, the trap's snapper-bar is still positioned on the "set" half of the trap, not the "tripped" half where the bait-pedal is located.
When the panther gets shot in the tail, a 1000 Hz tone goes off. This could easily be passed over as a technical problem.