When Alexander goes into the far future (635,427,810 AD), there are palms/ferns waving in the breeze behind him. When the camera angle changes to show us what he is witnessing, the whole area is void of vegetation. Even behind or next to the Time Machine.
At the beginning of the film, which is set in 1899, Alex talks to Filby about his correspondence with patent clerk Albert Einstein. However, Einstein was still in school and did not become a patent clerk until 1902.
When Alexander first meets the head Morlock and gets
strangled by him, you can easily see Jeremy Irons' fake fingernails coming loose and revealing his real ones. Also during the fight scene, in several different places you can see where the white make-up on Jeremy Irons' face ends and his un-make-upped face begins, usually around or behind the ears.