The film completely misrepresents the languages being spoken at the time. In 1357, when the film takes place, neither modern French nor modern English would have been spoken. The English would have been speaking Middle English (a language closer in pronunciation and vocabulary to Old English) and the French would have been speaking Occitan - a combination of Middle French and Latin. Certain members of both sides would have spoken Latin, especially the clergy. Michael Crichton details these languages in his book but the film ignores them.
When Kate and Marek are examining the monastery cave-in, they see a decorated section of the wall, which is damaged. When Kate and Chris go to the same section of the wall in 1357, it is decorated differently, and they break out a larger section of wall than what was missing in the present.
After Chris, Kate, Marek, Professor Johnston, and Gordon escape the manor house, all five can be seen stepping on to a balcony. The next shot reveals that all are stepping on to the balcony but Marek, who stops to go and rescue Lady Claire.
After Lady Claire and Marek kiss for the first time, she wipes away a tear, in the next shot, she put her hair back. This could not be done in one move, her hand is at eye height, and after that its on the top of her head.
After the group has walked into the time machine, we see Kramer and Doniger run up to the control room. In the next shot, Kramer can be seen next to the machine, just as Gordon asks Marek to change position.
When Chris and Kate are in the monastery in 14th century France, and first discover the tunnel and start to crawl through it, one of them knocks over a candle. In the next shot it is back standing upright, as if it was never knocked over, without anyone picking it up.
When explaining to the group how they would travel to 1357, it is explained that the fax machine was developed 30 years ago. In fact, it was first patented in 1843 by Alexander Bain, and commercially introduced and patented 119 years later in 1964 by Xerox Corporation.
While the English contingent is moving in the castle La Roque, we see stakes planted outside the castle, this was not a battle tactic in 1357, in fact the first stakes that were used by English were actually few years before the battle of Agincourt in 1415
Just after Doniger kills Kramer in the present, we switch back to the battle in France where Marek watches through a barred window as Claire is about to be hung. The whole grate is supposed to be set in a solid frame, but it moves. The "iron" bar on the right bends and wobbles.
The goof items below may give away important plot points.
After Decker kills Gordon with his sword, he returns the bloody sword to its sheath without cleaning it. A swordsman would never do this, as the blood could not be cleaned out of the sheath and the oxygen in the blood would cause the sword to rust.
When they were already fixing the "time travel machine" because of the explosion of the grenade. The LCD they used to determine the time left wasn't even scratched or damaged and all of the other equipment there were all damaged.