Continuity mistake: The letter D scratched into the pop up book is in white when first written. When shown again later, it's written in black.
Deliberate mistake: Paddington puts a red sock in the load of prison clothes which turns all their clothes pink. However, it was a single red sock in the "uniforms" machine, but in the next scene the entire prison is wearing pink clothes now. The machine is nowhere near big enough to wash all the uniforms at once - the pile we see is huge.