When playing poker in the opening scene, Harry Kim claims to have 'two pair' and wins the round. Prior to his claim, he was clearly seen holding two aces and three queens making a very high full house, which is a way better hand than two pair. Well, actually, he's shown holding two aces, two nines and a queen - indeed two pair. It was Tom Paris who declared having a full house (though it wasn't shown) and would have won the round over Harry if they weren't interrupted and pulled away from the game.
During the poker game, Chakotay places a bet, which is raised by Kim, who is sitting to his right, then raised again by Neelix, who is sitting to his left. The betting should have proceeded clockwise, from Chakotay to Neelix to Paris to Kim.
Lieutenant Commander Tuvok states that the U.S.S. Voyager will not be able to go to warp if the navigational deflector is removed. This is not the case, as the U.S.S. Voyager has a secondary navigational deflector.
Among the Borg children, Mezoti (the only Borg girl besides the infant) has full-length hair, Azan and Rebi have badly cut hair (or simply dirty), and Icheb is prominently bald. They are brought aboard Voyager to stay, but in that short time (mere hours), while Harry begins his recovery in sick bay, the Doctor also had time to remove most of the children's implants. Among his procedures, he also restores Icheb's hair to an attractive male growth (by human standards). Effort has also been made to get all these children washed, well-groomed and well-dressed as soon as possible. That's an impossible amount to accomplish in a few hours, in addition to wasting time on their superficial appearances while the ship needs repair, the Borg alcoves adjusted for the children, and the Borg cube (presumably) picked over for its data and technology.
At about 31:46, Janeway asks Tuvok how long it has been since he lost contact with Kim, and Tuvok replies "Four or five minutes." It has been long established in the series that, as a Vulcan, Tuvok speaks precisely - a comment that vague is completely out of character for him.
When Janeway re-negotiates with a Borg child, a close up of the Captain reveals a missing pip from her neck. The missing pip looks as if it fell off or was accidentally pulled off in a previous take.