Continuity: When the scouting party first enters the Event Horizon, Captain Miller states that the "Place is a deep freeze. We've got ice crystals everywhere." A few moments later, a plastic bottle of spring water is seen tumbling in zero-gravity in that area of the spacecraft, and the sound of liquid sloshing around in the bottle is heard. Of course, the contents of the bottle should be frozen solid if it's a "deep freeze", and it's not even remarked upon by the crew-member who examines it.
Factual errors: The various surgical implements in the medical bay of the Event Horizon are hung on hooks in the open air rather than stowed away in sterile conditions.
Revealing mistakes: Near the end, when Cooper watches the "blood" flowing above the ceiling lights, the front of the flow does not change shape at all and also, just before the camera changes, briefly jumps backwards, revealing it to be a computer effect.
Continuity: Despite being washed away in a flood of bloody water, in the following scenes Stark is mostly dry and whilst bloody is a lot cleaner than would be likely.
Audio/visual unsynchronized: In the scene where Justin is touched by something in the black gateway, you hear him say "Oh, shit!" but his mouth never moves.
Continuity: Just after helping Weir to his feet and as he turns away, you can see that D.J's shorts are completely dry on his backside, despite being in a tank of liquid for the last 56 days and being visibly dripping wet from the front.
Factual errors: When we first see the Event Horizon, it floats among clouds. No object can remain in orbit within any atmosphere. While Neptune's gravity is 1.19 times Earth's gravity, the near-supersonic winds of the atmosphere would make navigation difficult and a mere orbit near-impossible.
Continuity: On Captain Miller's shirt, his first initials are shown as being S.A. whereas on the door to his bunk, they are shown as being S.J.
Factual errors: Blood would have dried in seven years' time. Liquid blood droplets would be nearly spherical due to surface tension, like the coolant.
Continuity: The Lewis and Clarke crew enters stasis on the way to Neptune, made necessary because of the "30 Gs of acceleration" they will endure for the trip. When they arrive at Neptune, however, there are coffee cups and other debris on the tabletop, loose chairs, etc., in the same position as they were before the trip. This is not consistent with sudden and severe acceleration.
Crew or equipment visible: Studio space/backs of other sets briefly visible through holes in the "meat grinder" tunnel when the fire races through it.
Revealing mistakes: In the first scene featuring the crew in their residential barracks, Dr. William Weir pours a 'cup of coffee' for an off-screen crew member. Clearly, the thermos contains a clear liquid rather than a coffee colored liquid.
Factual errors: When Dr. Weir plays the record of the emergency signal containing the "Liberate me" bit, D.J. says that he can't make out the rest of the message, but Dr. Weir always stops the tape immediately after Liberate Me has been spoken, so D.J. wouldn't have been able to hear any other part of the message to begin with.