Montag's hair in the final scene is different than in the rest of the film because Oskar Werner wanted to create a continuity error to show his dislike of director François Truffaut.
While the foliage indicates that most of the film was shot in late winter into early spring, the trees are in full leaf as the fire engine is going to Montag's house.
In the first scene in the monorail, the view through the windows show they keep passing the same house.
As the firemen leave the apartment in the first raid, the sack is half full of books. The bag they toss over the balcony is twice as full.
When the books are being burned in the beginning of the movie, some books that are on the ground suddenly appear in the fire pit even though nobody moved them.
After Montag comes out of the first raid to burn the books, the placement of the fire protective clothing (helmet and gloves) are unnatural movements and appear to be a reverse run of film footage. This is further compounded by the fact that he walks backwards to get the flamethrower which has flame entering the nozzle instead of leaving the nozzle.
When Montag and Clarisse are on the elevator, you can briefly see the director through the mirror.