The flashbacks to season 3 show Janeway with the new, short haircut which she did not have yet.
The flashback sequences are set eighteen months in the past, concurrent with late season 3 and Tuvok would have been a lieutenant - yet he has his season 5 rank of lieutenant commander.
Although the flashback take place eighteen months previously, when season 3 was happening, Tom Paris' hairstyle doesn't match his style at the time.
Kes doesn't appear in any of the flashbacks to season 3, even though she was still on the ship and serving as The Doctor's assistant at the time.
Janeway's attitude towards the Doctor, explaining that he is not a person and is more like the replicator than he is a human being, is usually callous and goes against previous stories where she treated him as a sentient person and encouraged him to explore his individuality.
The Doctor exclaims that the Big Bang occurred 20 billion years prior, but cosmologists have since refined the estimate the Big Bang to have occurred 13.8 billion years ago.
When the shuttle is under attack, the Doctor beams the invading alien back to his own ship. Transporters don't work through shields, which the alien ship must have had raised.
In order to catch who's been tampering with his memory files, the Doctor sets up a holo-imaging camera aimed at the sickbay doors. The camera catches Captain Janeway tampering with the Doctor's system files. The camera itself is in plain view and lights up when capturing images, yet somehow Janeway doesn't notice it.
When the Doctor first regains some of the memories that were isolated, he has flashes of scenes in which he himself can be seen, rather than the memories being seen in first person POV. While these could mostly be chalked up to a stylistic choice, at least two of the flashes of memory are in first person, but one of them is from the perspective of Ensign Jetal as she converses with the Doctor, rather than the Doctor's own perspective.