This is supposedly the first time that Voyager encounters the Caatati; however, Neelix states that Voyager made contact with the Caatati in season 2 while reviewing the communications logs.
During the warp core accident, B'lanna's PADD she placed on the railing shifts to different positions. Also that same PADD should have fell off the railing and into the warp core silo during the turbulence.
The helmets of the environmental suits of Paris and Torres are lit up from the inside. If this were done with real suits, the lights would be reflected on the inside of the faceplate or visor, making it hard for the wearer to see. Unfortunately, Hollywood ignores this inaccuracy so the faces of the actors can be seen, rather than the dark faceplate when the wearer is viewed from the outside.
When the shuttle Cochrane explodes, Tom and B'Elanna watch it from a distance, but wouldn't the debris from the resulting explosion be hurled in all directions at a tremendous speed? Tom and B'Elanna would eventually be hit by the debris, being that they are unable to get away and don't have any way to protect themselves from the projectiles.
When Torres and Paris beam into space and the shuttlecraft explodes, they both turn their bodies to look at it then turn back to look at each other, which would not be possible.
When Torres and Paris drift in their environmental suits, Paris' speech and movements (and, occasionally, Torres') are slowed, a common trope of zero-gravity in movies and television; however, there is nothing about being in a zero-gravity environment that would cause a person to move or speak more slowly than in regular gravity.
It would seem more plausible the space suits were damaged from debris from the shuttle explosion than an ion surge.
Torres and Paris beam out into space. They float adrift with seemingly no tether between them until the script requires them to literally pull themselves together to interplex the com systems of both spacesuits. It's hard to catch, but Paris tethers his suit to Torres' just before teleporting.
Towards the end of the episode the nacelles are lit up as if they've got warp power. However they don't have warp power because they ejected the core so the nacelles shouldn't be lit up at all.
Once the aliens regain a positive association with Voyager, why doesn't Janeway ask them to rescue her crew? The aliens even know about the accident but offer no assistance.
When Paris and Torres get into the environmental suits, the one for Torres is obviously made for a female judging by the breastplate design. It seems odd to have one gender specific emergency evacuation suits on a shuttle.
Just before Tom Paris and B'Elanna Torres beam themselves out of the exploding shuttlecraft, Tom asks the computer to relay their coordinates and send a distress call to Voyager. The computer does not respond at all. B'Elanna says this is due to the communications system being down. Tom then states that the transporters are still online. He then asks the computer to 'energize' and the computer completes his request. Why would the computer not be able to respond to the first request at all but then oblige the second request?
When Torres, the Chief Engineer, orders Paris, a Bridge Officer, out of Engineering, he says "I outrank you."
She is the Commanding Officer of Engineering, Paris isn't even assigned there. In a chain of command, his rank would be irrelevant.