Jesse and Celine walk towards the back of the train heading for the dining car. As they enter the dining car, the train is now traveling in the opposite direction, backwards.
When the two meet on the train and engage in conversation, the views outside the train don't match when we cut back and forth between Jesse and Celine.
As Jesse and Celine are leaving the homeless poet, his cigarette is burning close to the butt, but in the next shot his cigarette is whole again.
At 19:45 you see a tramway at Schottentor station. A few seconds later Jesse and Celine are on a tramway about a mile away from Schottentor (at Karl-Renner-Ring) and heading towards it.
When they first meet in the train, Celine says she is heading to Paris, because her classes start next week... At the end they reveal the date, and it's 16th June. Which doesn't make much sense, classes usually start around September/October....
At the club where two guys (director cameo) and two girls are playing foosball, on the girls' side no one is holding the control knob for their goalkeeper. In fact the girls are shoved with one row to the right in order to be their opponents better visible.
Jesse and Celine are said to come from Budapest to Vienna, but in the train scene, there are forest and hills to be seen outside the window all the time. But there is no such landscape along the railway between Budapest and Vienna. In fact, the landscape looks more like the railway line west of Vienna, in the direction of Salzburg. This suggests that the movie was rather filmed there.
In Vienna, Jesse talks about his obsessive relationship with "Miss July, 1978" of Playboy magazine, then asks Celine if she knows Crystal. Playboy's Miss July 1978 was actually Karen Morton, cousin of 1970s model Elaine Morton.
In the beginning of the movie Céline speaks English with a heavy French accent. As the movie progresses she gradually loses her French accent and has hardly any left by the end of the movie.