After losing their warp drive, the warp core shuts down but the warp nacelles still glow blue as though the warp drive is still on-line. The glow given off by the warp nacelles is the glow of the warp coils when energized. With the warp core down there is no way to energize the coils, so the nacelles should be dark.
As Voyager gets pulled into the void, Neelix and a crewman fall to the ground in the mess hall while the large dining table topples over from the turbulence. A flimsy serving cart next to it doesn't so much as wobble.
Neelix seems to forget that he has a ship of his own in the cargo bay. Since they need deuterium to power the warp engine, nobody raises the fact the his engines could have provided it for them.
When Voyager is first attacked in the void Chakotay says "They've transported materials off decks 5,7, and 8." Before that it's shown that materials are being transported off deck 11 in Engineering as well.
The lights on Voyager shouldn't take more than a minor amount of the total power. It doesn't make any sense to turn them down while still using shields, replicators and weapons.
During the end scene where the alliance ships go their separate ways, Voyager engages warp and it's warp nacelles move to a far greater angle than the usual ~35° seen previously.
Paris states that deuterium (heavy hydrogen) is found almost anywhere; yet, in episode "Demon," he and Kim chance going down to a Class Y planet to find hard-to-find deuterium.
The Doctor repeatedly mispronounces the French name Fantome. His pronunciation sounds almost Italian.
As the episode progresses, Voyager is running on emergency power with essential life support only. Even the lights are dimmed in order to conserve energy. And yet the Doctor is playing opera music in sickbay.
The ship Valen is on is reminiscent of the Kraylor ship nightingale from the seventh season's "Nightingale". Valen is Annari therefore he should be on an Annari warship not a Kraylor vessel.
Although Chakotay is a vegetarian, in the opening scene, he is served Luhvian quail.