The episode goes on and on about breaking the trans warp barrier. But in Star Trek III Search for Spock, which was set 100 years earlier in the timeline, Scotty was forced to sabotage the trans warp drive of his new ship, to allow the Enterprise crew to steal the ship from space dock.
While Voyager is pursuing Tom and Janeway in the stolen transwarp shuttle, the computer announces that the ship is exceeding maximum warp velocity and structural integrity will fail in 45 seconds. The ship is said to be traveling at warp 9.9 at that time. It has previously been established that maximum cruising velocity for Voyager is warp 9.975. Maximum cruising velocity is the highest speed a ship is capable of for extended periods; it can travel for shorter bursts at higher speeds. Traveling warp 9.9 would not put the ship in any kind of danger.
Tom and Harry try to break the Warp 10 barrier. In the process they say it's a theoretical impossibility and that no one has gone that fast. In That Which Survives (1969)(#3.17) and Star Trek: The Next Generation (1987) the warp 10 barrier is apparently broken.
When Janeway approves the transwarp test flight, she mentions Tom Paris joining and elite group of pilots. Orville Wright, Neil Armstrong and Zefram Cochran. They failed to mention two pilots of merit - Charles A. Lindbergh (the first to fly across the Atlantic Ocean) and Chuck Yeager (the first to break the Sound Barrier).
At one point during his mutation, Tom removes his tongue, impairing his speech as a result; yet, when he asks the Doctor later to release him from sickbay, he clearly says "please." Without a tongue, he wouldn't be able to produce an 'L'. Also, his tongue can actually be seen on several occasions during that scene.
When the mutated Paris carries unconscious Captain Janeway and gently puts her down, the Captain holds her head steady, instead of having it hang down, as it does for an truly unconscious person.
When Tom tries to attack Janeway in Sick Bay she knows that there's a force field in place but yet she can be seen moving back as if she thinks the actor Robert McNeil is going to actually hurt her.
The transmitter used by Jonas to talk to the Kazon is the same prop as the neurotransmitter link used in the episode "Unity."
B'Elanna, Tom and Harry struggle to figure out why the computer simulation of reaching warp 10 causes the nacelles to tear off the shuttle, yet if the computer programming predicts this, the computer would be able to tell the crew why. It couldn't be a mystery.
Tom's mutation into an amphibian or reptilian creature starts off with an allergic reaction to water. It would be interesting to know how a water-resident creature can survive with a water allergy.
When Tom makes his first Warp 10 test flight in the shuttle, Tuvok announces his speed as Warp 9.9. He then states that the shuttle is exceeding Voyager's maximum speed; however, in the first episode of the series, Lt. Stadi establishes that Voyager has a maximum sustainable speed of Warp 9.975; therefore, at Warp 9.9, Voyager could easily keep up with Tom and the shuttle.
When Tom collapses in the mess hall, Torres calls Sickbay for a medical team. There are no medical teams on Voyager. The medical staff consists of the Doctor and Kes, who, since she does not appear until Paris' mutation has progressed considerably, presumably is not on duty at the time.
Chakotay makes the decision to leave Paris and Janeway's amphibious offspring on the alien world. Many life forms, especially humans, are very helpless in their early development and dependent on their parents for protection and nourishment. Chakotay may very well have been condemning those children to death by leaving them behind. Federation ethos would seem to say that if one creates life, one has a duty of care to that life.
Tom Paris refers to the babies he and Janeway had as "alien offspring." The offspring are not alien, but an advanced form of human.