While in engineering, Seven fires a phaser rifle at her imaginary foe. Assuming the phaser rifle itself was not an hallucination, the door behind her imagined target should be singed, yet when we see it moments after the doctor arrives, there are no burn marks visible.
When Seven and the Doctor are in the holodeck participating in the crew mingling program, they rush out for a ship emergency. They hurriedly exit through the mess hall doors, but they're not really in the mess hall, they should have exited via the holodeck doors. Although it has been shown through a number of holodeck simulations of certain rooms both on and off the ship that the holodeck exit door is quite often just beyond a door in the program (so the program can include the full room, presumably).
When Seven is reading off Paris' vital signs, the tricorder provides his body temperature in Fahrenheit. Since the metric system is used in all other Starfleet units of measurement, it is unlikely body temperature would be any different.
The goof items below may give away important plot points.
Near the end, Seven cuts life support to power the engines to get the ship out of the nebula in the next eleven minutes, and her hallucinations point out that she can't survive without oxygen and heat. On a spaceship, getting rid of heat is more of a problem than keeping it, and there would be sufficient oxygen left-- not just in the ship as a whole, but it a room the size of the one she as in-- to keep her alive for much longer than eleven minutes. Seven would know this, and she certainly would not have passed out.