My favorite is in "Time And Again" when The Doctor examine Kes after her vision of the destroyed planet seem unaware of the facts that:
1. Kes and Neelix arrived to the ship in "Caretaker" and joined the crew shortly after.
2. Chakotay and the other Maquis came on board and joined the ship at the same time.
I mean, according to the stardates, there are two months between the events in "Caretaker" and the events in "Time And Again". The Doctor did examine Kes, Chakotay and Torres in "Caretaker" and still he don't seem to remember that they had joined the crew. Now that must have been a serious malfunction in his program.
As for stardates, we also have the stardates in the episodes "Lifesigns" and "Investigations" which are totally wrong. According to those, the events in "Investigations" took place before
the events in "Lifesigns" which is impossible.
And we also have "Threshold" which is a whole long contradiction. Paris breaks the threshold for warp speed, almost dies, turns into a lizard, abducts Janeway who is also turned into a lizard and they have lizard “children” and no one talks about it or jokes about it later!
It's totally forgotten in later episodes.