(at around 14 mins) When Elizabeth arrives at the Department of Health, a clock shows 8:44 (am presumably). At the end of the scene, after the Asian man bumps into Elizabeth, a clock on the wall behind him clearly shows 4:30.
The curliness of Donald Sutherland's hair changes quite drastically between scenes. (According to co-star Veronica Cartwright, the hair and make-up department had to set his hair with rollers every day.)
(at around 28 mins) During the "accident" scene a gray pickup truck appears under the "Ringside" sign where a white car earlier appeared.
(at around 51 mins) Just before rescuing the sleeping Elizabeth, Matthew is hiding in the slightly open bedroom closet. His face, not even quite outside of the closet, is clearly illuminated from directly below. Yet when he emerges into the room, the only light source anywhere around is a bedside lamp that couldn't possibly have cast light on his face in that manner.
(at around 28 mins) When the running man has his fatal "accident," two cars cross the intersection twice: a maroon Beetle with gray front wheel guards and a green car. We don't see the impact, hidden by a green commercial van, but from the impact timing, the second Beetle had to be the vehicle to strike him. The policeman arrives with the second green car. As they turn right on red, the vehicles parked across the street from the accident suddenly change. The green car has diagonally parked at the scene ahead of the victim, its red parka-wearing driver looking on, but the Beetle is nowhere to be seen.
(at around 1h 40 mins) The ship being loaded with pods was in dry dock; the entire propeller is clearly visible. Ships are not loaded in dry dock.
(at around 1h 45 mins) Up in the "flyloft" of the factory, Matthew sees a fire axe and decides to run over to it - after walking past one right as he climbed the lower ladder. However, it's possible he didn't realise he'd need it at first until he climbed higher up to survey the ropes and cables holding the lights in place, and secondly he still had another ladder to climb and probably didn't want a large, heavy axe hindering his climb.
(at around 1h 40 mins) When Matthew says to Elizabeth "Oh God, are you alright?" after falling into some overgrown brush, the distinct sound of brief and unexpected flatulence can be heard followed by "a factory" from Elizabeth. However, this outdoor scene was obviously done with ADR (automated dialogue recording) and so all of the dialogue and found effects that are actually heard would have been added long after the scene was shot. The "flatulence" sound actually sounds more like some industrial noise in the distance associated with the dock setting.
(at around 29 mins) At Kibner's book release party, as Jack and Matthew are walking while Jack is putting down Kibner's work, he turns abruptly to engage the woman before she begins to verbally disagree with his comments about Kibner's work. However, if you watch the scene closely, you can see the woman stopping Jack with her left hand and removing it from his arm as she says "How you say that about a man like Kibner?"
(at around 18 mins) When Sutherland is stir frying, there is no steam rising from the wok, even though one can hear the sizzling of the cooking. In fact, not only is the wok not hot, the vegetables have the appearance of being frozen as they are stirred in the wok.
(at around 10 mins) Early in the film when Geoffrey and Elizabeth are talking and we only see their reflections, Geoffrey's mouth isn't moving.
(at around 1h 5 mins) The cameraman is reflected in the phone booth window while Matthew Bennell is inside.
(at around 1h 15 mins) When pods attack Matthew and the others at Matthew's house, four bodies form in the yard, yet Nancy isn't asleep. She's shown wide awake, and she's the one who wakes the others when she goes outside and sees the bodies growing. If the pods can only attack when the human victim is asleep, there should have only been three bodies.
If the alien spawn arrived on earth from another planet surely they would have landed in many different countries not just the USA, so there would be no need to load pods onto ships for export.
(at around 1h 45 mins) It is established in earlier dialog that there is no emotion left when the humans are reborn. Despite that, when Matthew pushes an attacker from the rafters in the "pod farm," the man that falls screams in fear.