Voyager arrived in the Delta Quadrant on Stardate 48306.6. When Kes travels into the past, she arrives 56 days 17 hours after Voyager's arrival in the Delta Quadrant on Stardate 48447.65. Voyager did not make contact with the Vidiians until Stardate: 48532.4 during Phage (1995), 90 days after their arrival in the Delta Quadrant.
Tuvok is shown wearing Lieutenant Commander pips (2 solid, 1 hollow) during the past scenes, which take place during Season 1. He wasn't promoted until Season 4. Furthermore, Lieutenant Carey refers to Tuvok as Lieutenant (his correct rank at the time, but not his correct insignia). This is a well known mistake from the actual first season where Tuvok wore the Lieutenant Commander pips even though he was just a lieutenant. It was later corrected during season 2.
Kes spills coffee on the Captain's desk and a data pad. As she wipes the spill, the data pad comes and goes as the camera angle changes.
When Neelix is about to give coffee to Kes, he holds the smaller carafe. When the camera changes, he holds the larger one and starts pouring coffee into the smaller one.
When in the past after Kes has traveled back in time. Captain Janeway says to Commander Chakotay "Do I detect a note of sympathy?" Captain Janeway had said way back in season 1 to the Vidiians in the episode "Phage" "I have a great... sympathy for what your race has endured..." This statement is contradictory considering she (Captain Janeway) didn't have any sympathy for them in the past that Kes traveled to in "Fury".
Near the end, Older Kes sees a holographic image in engineering that younger Kes recorded. There were no known holographic projectors in Engineering, but that's not to say one couldn't be privately installed in the three years between events in the new timeline.
When the younger Kes is lying on the floor of the hydroponics bay after being rendered unconscious by her older self, a reflection off the glue that attaches her prosthetic ear is visible.
In The Gift (1997), Kes had the ability to send Voyager 10,000 light years closer to home. If she had that same ability, why did she need passage from the Vidians when she could simply send her younger self back to Ocampa?
Too much time goes by before the Captain is told about Tuvok's seizure. Since he's a member of the bridge crew, and there is a serious situation going on, the Captain should be notified immediately.
The entire show is a temporal paradox. If the older Kes doesn't travel back in time, then there is no reason for her to make the recording of her younger self to tell the older Kes not to go back in time.
Captain Janeway tells Tuvok "it's not long before you hit the big three digits," implying that he is not yet 100 years old, but it was made clear almost four years earlier, in Flashback (1996), that Tuvok was already 108 or 109 then; so, by this time he'd be 112 or 113.
When Janeway orders the shields modulated, Ensign Kim responds that the Vidians are matching their frequencies. Kim is the operations officer. Shields are controlled by the tactical officer.
The Doctor states that the Vidians are interested in Voyager because it is the only source of fresh organs within half a parsec, meant to represent a great distance. Voyager is capable of traveling that distance in a matter of hours, so it is not so great a unit of measurement as the dialogue implies.
Chakotay orders a full spread of torpedoes against the Vidian ship. Ensign Kim carries out this order. Kim is the operations officer. Weapons are handled by the tactical officer.
After Tuvok informs Captain Janeway that he encountered a half-Ktarian girl calling herself Naomi Wildman, Janeway muses that Ensign Wildman's husband is Ktarian and wonders if Tuvok may be having premonitions. Neither of them think to verify the possibility by actually asking Samantha Wildman if she is pregnant.