Young Helge was urinated on and wears the same clothes throughout the episode. Then he goes to tutoring like nothing happened, stinking of urine, and nobody notices.
The Volkswagen Beetle used by Egon Tiedemann in 1953 is a later model (the square rear window was not introduced until 1957) to which older fenders without turn signals have been mounted. An authentic Beetle from the period would have a split rear window ("Pretzel") or an oval one if built after March '53. Morover, police cars at the time were not yet painted in a green/white pattern.