After Voldemort kills Lily and James Potter and is defeated by baby Harry, Hagrid retrieves Harry and they travel by Sirius’ flying motorbike from Godric’s Hollow to Little Whinging. Harry is asleep by the time they meet Professors Dumbledore and McGonagall outside of Number Four, Privet Drive, the home of Lily’s sister and her family. Despite McGonagall’s and Hagrid’s worries, Dumbledore produces an explanatory note and leaves baby Harry to grow up in the Muggle world.
The actual "real world" calendar of 1981 shows that October 31 was a Saturday and November 1 a Sunday, which doesn't match the statements in the book.
Dudley's birthday is in June, as we'll see in the next chapter. Harry's birthday is July 31. On this day, Dudley is about 16 months old and Harry is 14 months old.
This happens around midnight on November 1. Harry's family was attacked "last night," on October 31, so at this point Harry has been with Hagrid for about twenty-four hours. We are not told where Hagrid went with Harry for all this time. Surely Hagrid hasn't been just flying around Britain for a whole day, waiting to meet Dumbledore on Privet Drive. And what was Dumbledore doing all day? The common assumption among fans is that Dumbledore spent the day preparing things in and around Privet Drive for Harry to be safe there, including stationing Arabella Figg a few streets away. Hagrid, it is reasoned, took Harry to somewhere safe, possibly to Hogwarts, to wait for the signal that all was in readiness.
The flying motorcycle belongs to Sirius Black, according to Hagrid. But how does a normal-sized man ride a motorcycle which is huge enough to be ridden by Hagrid? It is likely we're seeing an example of a magical effect which the Lexicon dubs "wizard space," by which things expand to fit the need. The flying motorcycle also raises the question of why it's okay to fly a motorcycle but not a car. In CS6, Arthur Weasley gets into considerable trouble for enchanting a Ford Anglia to be able to fly.
In the original text, Hagrid says, "I'll be takin' Sirius his bike back..." In 2004, this was changed to "I best get this bike back" so that the story fits the way the character of Sirius Black developed in subsequent books.