Between Raj making his penguin comment and Mrs. Davis picking up her food and walking away, she starts to open her mouth. It is suddenly closed in the next shot.
When Howard gets mad and stabs Raj's pot pie, a large piece of carrot pops out. It disappears in the next shot.
Leonard and the other people on the boat on the North Sea expedition play the drinking game 'Iceberg', whenever someone sees an iceberg. There are no icebergs in the North Sea. The North Sea is situated between the UK and mainland Europe, too far south for icebergs.
In the "Serial Apeist" clip, when Penny showers some of her hair is tucked behind her right shoulder. When the ape appears, she starts to turn around and there is hair in front of both shoulders. "Serial Apeist" can be assumed to be a low budget movie where they take even less care than The Big Bang Theory does about continuity.
Sheldon suggests that Penny calls Leonard. He only mentions after the fact that it is actually in the middle of the night where Leonard is. This makes it a strange suggestion on his part to call at that time at all.