It begins to snow as Javert prepares to commit suicide. This part of the story takes place on 7 June, 1832 (the June Rebellion took place on 5 and 6 June, Javert's suicide occurs the day after). It did not snow on that day in Paris. Snow in June in Paris would be highly unlikely at any time.
Valjean always makes a big production of keeping the gates and doors to his and Cosette's home locked, yet when Javert returns him home to say farewell to Cosette, he walks straight through the front gate without unlocking it.
Marius makes up a story for Cosette that Jean Valjean is traveling to London, then to Egypt. Later, Valjean is shown composing a letter to Cosette and Marius claiming to be in Cairo, Egypt. Marius and Valjean never discussed the cover story of traveling to Egypt, so there should be no reason for Valjean to compose a false letter to sell a story he was not made aware of.