When the phone tracing is being set up in the Barrington house, Officer Cheets hangs up the handset on a phone. In the next shot it is still in his hand.
After Beary and Henry get into the bus to go get the band, there is a shot of Beary hanging out the window of the side of the bus. In the shot, the bus is clean, but this is before the bus goes through the car wash. The next outside shot of the bus shows it dirty.
When the bears are being spun in the booth in the diner, they are alternately seated/dancing between shots. Tennessee also alternates between wearing a sweater and a vest.
When Henry is talking to Ted on the pay phone in the background you see the bus dirty just after they wash then when the bus pulls away once again it is clean just like when it came out of the car wash.
When going through the car wash, Officer Cheets loses his mustache once before it getting stuck to the windshield of the car. When he goes through the spinning washers, he briefly has no mustache, but when he comes back out he suddenly has it again for it to get stuck to the windshield.
When Ted is in the boat on the way to save the rest of the crew, he turns the corner the boat goes up on one wheel and the two extra wheels underneath that make the stunt possible are briefly visible.