At the beginning of Father's reprimand, he shouts out a phrase that many have eerily assumed to be "Wha-What the shit?!" Scary isn't it?
Speaking of which, in the 2002 version when Pingu is ringing the bell when playing doorbell ditch to make his father leave the bathroom and answer the door, it eerily sounds like he's saying "Goddamn it!"
Earlier in the episode, Pinga ended up pissing on the ground near the bar after Pingu ordered two drinks for her. He tells her off and sends her home to her potty, where she finishes it up. Then the tables are turned when Pingu takes the third drink and realizes that he has to piss.
Unfortunately, SF DRS noticed the Unfortunate Implications, and swiftly banned it from rotation and from foreign broadcast. It became so popular, the crew slipped references to this in later episodes as well; one episode from season three lampshades the urination scenes when Pingu goes to the bathroom while in bed.
In "Pingu Quarrels With His Mum", Pingu throws a tantrum when he is repeatedly denied to play at his friend's house. In response, Mother gives him a slap in the face. This was deemed so offensive that the scene was cut from the BBC.
"Pingu Runs Away" has something similar to this. After Pingu refused to eat his dinner, he rocks his chair and ends up pulling all the food off the table. His parents are so furious that Mother approaches him and ends up spanking him on the ass. This was the only episode with this sort of instance.
Pingu and Robby appear to have examples of Ho Yay. In "Pingu Plays Ice Hockey", Pingu and Robby nuzzle on each other.
Pingu's father appears to believe Smoking Is Cool; he had a pipe in his mouth in many of the older episodes (and in the episode where Pinga was introduced he even had his pipe taken away by his wife!).