Factual error: On page 25, it mentions that the boa constrictor at the zoo winked at Harry. Snakes don't have eyelids at all, so it's impossible for them to wink.
Factual error: When Harry is with the Dursleys in the run-down shack, he realises that Tuesday is his birthday. However, in 1991, July 31st was a Wednesday.
Answer: Harry has already experienced a few magical incidents, as children from Muggle families usually do. For example, changing a teacher's wig hair to a blue color. If Dudley's birthday is on a school day, his parents probably don't want the risk of a problem at school. It's easier to make Harry stay with Mrs. Figg all day.