The Doctor calls out the constellation Hercules, saying it's named after a character in ancient Greek myth. He's wrong, and it's a common mistake. Hercules is a Roman name. The Greek name is Heracles, named after Hera, queen of the gods.
When Danara Pel is first transported to sickbay, her eyes are open and can been seen flickering as the Doctor examines her. When the shot changes, her eyes are shut.
At about 6' in when Chakotay is reporting on the Vidiian to Janeway, actor Robert Beltran (Chakotay) mispronounces the name of the species as "VID-ee-un", when in all other episodes they are referred to as "vi-DEE-an".
When the Doctor makes it clear that Danara won't be able to see the rest of the ship due to her holographic body, instead of her visiting the rest of the ship in real life, she could have had the Doctor program the ship on the holodeck and visit the ship that way. It's made clear that the Doctor was able to do that in the season 6 episode "Lifeline."
Danara Pel has a rather large device implanted into her skull with multiple blinking lights, but neither the Doctor nor Kes notices it until the Doctor begins a very thorough examination on the side of her head.
The captain tells Kim to open a channel to the Vidiian vessel. He does so and immediately says 'No response.' He doesn't give any time at all for a response.