In the Eloi's time, the ruins of the library still have clearly visible, sharply incised inscriptions. Such carvings erode significantly after several hundred, or at most, several thousand years; after 800,000 years they should have been illegible, due to erosion from rain or wind, or (if they had been buried) chemical reactions in the soil.
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.
The motor-carriage that is seen outside the skating rink and later on the street by the flower shop, has current bicycle type tires (metal rims and spokes), most vehicles of the time had wooden rims and spokes, lined with rubber.
When the Vox says "Live long and prosper," it holds up its hand with the fingers in a "V" and the thumb next to the index finger. The Vulcan sign is properly done with the thumb away from the index finger so the hand makes more of a "W" shape. The salute is actually for the Hebrew letter Shin which has three points, not two. Leonard Nimoy (who is Jewish) saw the sign given during a Hebrew ritual and used it years later when an "exotic" sign was called for in his Star Trek role.
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.
When Alexander arrives on the date of May 24th, 2030, he is seen watching the "Future is now" on a large screen. When he unravels the rope that lets the "step-down" stairs down, a man in a white shirt and blue jeans can be seen slightly behind the time machine for a brief second, then he vanishes back under the machine when Alexander is walking toward the screen.
Most, if not all of the structures built in New York City around Alexander's former home on East 60th street are not present during the zoom out section of the 1899-2030 time travel sequence. Some of these structures include the Plaza Hotel, The Metropolitan Club, The Pierre, Hotel Sherry-Netherland, Ritz Tower, and Rockefeller Center.
The amount of geologic change that occurs in the movie over the span of 800,000 is far too great for that passage of time. Glaciation and valley formation shown in the movie would take place over millions of years, not hundreds of thousands.
Actress Myndy Crist, who is the friendly New Yorker who thinks Alexander Hartdegen's Time Machine is a Cappuccino maker, is listed in the movie credits as "Jogger", but in the entire scene she is unlocking her bicycle from a bike rack, thus her credit should be "Bicyclist", since she isn't jogging anywhere in the film.
In the generated fast-forward sequence, from prop planes to landing on the moon, the International Space Station was depicted as being in high Earth orbit, when in realty, it has never risen above low Earth orbit.
At the very beginning of the movie, a clock on the wall strikes three o'clock. In the next scene, when Philby reminds Alexander of his date with Emma, Alexander asks what time it is with Philby responding that it's close to five o'clock.
It is impossible for the moon to remain in scattered fragments after such a long time as 800,000 years. By that time, gravity would have caused the fragments to fall back together into one contiguous moon or to form a ring around the Earth. However, the later shot of the moon in the far-flung future shows that it is continuing to fracture, indicating that the detonation that cased it to fragment in the first place was much deeper than simply a few stray fragments, and the stretching between the two time periods shows that the pieces are becoming the aforementioned ring.
While we can only speculate about the imagined physics that allows the time machine to operate, we see that when the time traveller accidentally puts his hand outside the protection of his machine's 'force field' during travel to the future, the fingernails grow by at least five millimetres before he snatches his hand back in pain. This amount of growth indicates that his hand has experienced at least a month while outside the field. Since his blood vessels inside the field would only be supplying a few seconds worth of blood, his hand would be starved of oxygen and therefore dead and well into decomposition by the time he manages to get it back within the field. His only option would be immediate amputation to prevent gangrene in his arm.
Given that whole years pass in a matter of seconds from his perspective, Alexander shouldn't be able to see how the medallion falls to the ground in normal speed (nor hear the sound it makes when it impacts on the ground).
When Alexander asks the VOX unit about time travel and it responds with information about various scientists, Alexander himself is one of them listed, and he asks VOX about Hartdegen's theory for time travel. VOX rejects the reality of time travel, but given that he is speaking to Alexander, a scientist who went missing in 1899 and has now mysteriously reappeared in 2030, and because he has information about Alexander including the photograph next to the description, he should piece this all together and realize that Alexander indeed traveled through time.
When Alexander is unconscious and traveling into the future, the dials on the time machine seem to be spinning at a rate of around one million years per second. He would have far surpassed the year 802,701. Adjacent dials in the row also spin at the same rate, instead of at a "sequential times ten" ratio, and the left-hand three dials never change, even though the dials directly to their right are spinning rapidly. This shows that the dials were made to just spin, rather than count.
When Alex and Emma are being robbed in the park, she is shot and falls to the ground, so that her hat falls off very near to her head and slightly to the left. In the next shot, the hat is on the right hand side and far away from her body.
When Alex is traveling forwards in time and drops the photo chain, his fingernails grow a couple of centimeters on his right hand as he grabs it outside the machine's vortex. Upon the arrival to the year 2030 he still has long fingernails but after a couple minutes when Alexander enters the library it's clearly seen that his fingernails are accurately cut. In fact Alexander can be seen biting his own fingernails off shortly after exiting the time machine in 2030, this can be seen from 27:06 to 27:08.
During Prof. Hartdegen's first talk with the VOX unit in the city, he clearly asks the unit for more info on temporal causality and temporal paradox. Both these phenomena are what the uber' Morlock explains to him towards the end of the film when he tells the professor that he cannot save Emma because it would create a temporal paradox. So, if the professor even had a passing knowledge of what those terms meant, he would already know why he cannot change the past and would have never required to go anywhere.
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.