When Harris drives down the stairs, his car is very dirty. Then immediately after, but before he drives through the sprinklers, it is clean again.
As Sarah tells Harris of her weekend plans with her ex-husband, her hands change position on the car door between shots.
When Sara plays the tuba over the telephone with her mother, they play in perfect sync. Presumably her mother lives in the UK. Given the distance between the UK and the US West Coast, the time it would take for the signal to travel back and forth would make it very difficult to stay synchronized. Her mother would have to play the keyboard early to account for the signal travel time, so it would appear synced on Sara's end as it does in the movie. But her mother would hear Sara playing with double the delay. Plus, if they both have their phones on speaker, the sound of the instruments would also start to reverb over the call.
Since 1988, with transoceanic fiber-optic cables, the delay is under 1/10th of a second which the human brain is too slow to notice.
The close up of the airliner's throttle levers towards the end of the movie shows that there are four throttle levers, one for each of the four engines. The next shot is of a taxiing DC-10 which only has three engines and would only have three throttle levers.
As Harris is driving south on the 110 freeway after the "Open Season on the L.A. Freeway scene", you see absolutely no traffic on the northbound side, even though it is mid-day.
In the credits Sarah Jessica Parker's character is listed as "Sandy" and not "SanDeE*".
As the car begins to drive itself, Harris breaks off the faux luggage rack bar. When he puts Sara in the car he drops the bar and you can hear it hit the street. Once they returned to his apartment, the bar is back where it should be.
Near the end of the film when signposts are shown scattered across the L.A freeways, some signposts are planted right in the center of a road.
After running into Sara and Roland in the museum, Harris picks himself up off the floor saying "I get that," but his lips are clearly saying something else.
When Harris tries to tell SanDeE* that he can't go to Santa Barbara, the busker (guitarist) at the left is playing non-stop but doesn't make a sound.
The museum displaying Mozart's quill misspells his middle name as "Amedeus" instead of Amadeus.