When The Master and Chang Lee are examining the Eye of Harmony, in some shots the pit that holds the Eye contains lots of dead leaves but in others it is completely empty.
When the Doctor is being X-rayed, there is no blood on his clothing. He was shot three times. The first shot hit around his right collar bone, which is still covered by his opened shirt during the X-ray, but the shirt should have been heavily blood-stained. Shortly afterwards, when he is being prepped for surgery, the shirt is blood-stained.
The entire ambulance/hospital sequence is a symphony of errors: A bystander would not be permitted to ride in the back of the ambulance, nor would his (or anybody's) consent be required to provide care to an unconscious patient with life-threatening injuries. Nobody was performing the routine care and monitoring that medics would have performed. An external EKG, and not an internal probe, would be used to assess the heart's electrical activity. The Doctor was not intubated, as he would have been for surgery. The cardiologist would have doffed her gown and put scrubs on over her underwear in the locker room, then scrubbed for surgery, rather than scrubbing first then being stuffed into scrubs over a ball gown.
In the operating room, one of the doctors make the classic TV/movie mistake. He shouts "He's flatlining!" (meaning that the heartbeat is stopping) but then use the defibrillator on the Doctor. Defibrillators are used to correct irregular heart rhythms, not 'restart' a heart.
At the start of the movie, when The Seventh Doctor seals The Master's remains shut with the sonic screwdriver, the head of the screwdriver is slightly out of focus. This is explained in a 2005 interview by Sylvester McCoy; he was holding it the wrong way around.
When The Doctor and Grace arrive back at the TARDIS and a police motorbike with a man astride it drives in through the TARDIS doors the base of the TARDIS that causes a rim on the door clearly vanishes leaving no change or gap between the TARDIS floor and the pavement outside.
In the German synchronization, Grace tells the assistant in the operation scene to play the CD from act 4 of Madama Butterfly instead of track four as in the English original. Madama Butterfly doesn't have an fourth act in any of its versions.
It's counterproductive to remove ignition keys from a motorbike you want to ride.
The Master was supposedly executed by the Daleks following his trial on Skaro. No doubt this is an American misunderstanding of the property, but the Daleks are not the sort of creatures who would bother holding a trial. Trials are a typically humanitarian concept that allows an accused person the right to prove their innocence following supposed wrongdoing, even if the accused's guilt was predetermined (i.e. a kangaroo court or "show trial"). The Daleks have no necessity to seem "fair" and would not bother with such a human concept. They would simply exterminate their enemies without the need for a trial or any form of justice system.
At Grace's apartment The Doctor says, "Don't you see, I have Thirteen lives", however his lip movements say "Twelve lives". (See trivia.)
Despite losing all of the possessions that were on his person after being checked into the hospital, The Doctor still produces his trademark bag of jelly babies twice. Where did they come from?
If Chang Lee's goal in accompanying The Doctor to the hospital and staying with him overnight was to steal his possessions, why didn't he just pick The Doctor's pockets when he was lying unconscious in the alley?
When Grace chases Chang Lee down the hallway, she screams for someone to stop him. A security guard can be seen walking out of a room, but just ignores what's going on, rather than pursuing the fleeing young man.
The party host makes the common mistake of saying that 1 January 2000 is the first days of the new millennium. The millennium started on 1 January 2001.