Some of the bars on Geordi La Forge's VISOR are slightly bent inwards in some shots; this is especially obvious when he encounters the simulation of Dr. Brahms.
Even though the crew is exposed to radiation (not yet lethal), they display no symptoms of radiation poisoning. A radiation field with enough intensity to kill someone within 26 minutes wouldn't cause a lot of the symptoms that long-term radiation sickness does (such as hair falling out, skin burns, lesions and severe weight loss); however, the crew WOULD experience severe nausea and headaches. Though it is possible that Dr. Crusher was giving the crew something to treat the symptoms, it is very unlikely it would be able to totally prevent symptoms.
Geordi runs the same simulation over and over, getting different results. Assuming the input values are not changed, the differences should not be possible with a computer simulation; however, even modern-day computer simulations often have "randomness" built in, to account for shifting variables. (The magnitude of the "randomness" is generally its own parameter set by the user/researcher and utilizes a Random Number Generator, or RNG.) Surely, a few centuries from now, such simulation methods will still be utilized.
When Picard fires the starboard thruster, the next shot shows an exhaust stream on the yoke of the star drive section; however, when Picard uses the port thruster, no exhaust shows.
In order to escape the booby trap, all power on the Enterprise, except for minimal life support and thrusters, is shut off; yet, during the escape sequence, lights are seen through windows all over the ship.
The optional subtitles mistakenly credit the violin music as "Hungarian Rhapsody by Franz Liszt" when in fact it is a solo violin arrangement of "Hungarian Dance #5 in F# Minor" by Johannes Brahms.
When Geordi and Christy are on the holodeck, the violinist is obviously not actually playing as he is holding his bow about an inch away from the strings.
After the captain returns from the Promellian vessel and is on the bridge, Riker is looking at and speaking to him. Riker suddenly stops speaking as if he hears an alert, but the alert signal, and Worf's verbal alert, don't happen till a couple seconds after Riker stops speaking.
Geordi says that the Enterprise's warp engines have tens of thousands of light-years on them; however, it has been established throughout TNG, Star Trek: Deep Space Nine (1993), and Star Trek: Voyager (1995) that it would take the average Federation starship from the late 24th century more than 10 years at maximum warp to travel 10,000 light years. The U.S.S. Voyager was stranded 75,000 light-years from Federation space, and it was revealed that even if it were possible to maintain maximum warp for the whole time (which it is not) it would take 75 years to return to the Federation. That averages about 10,000 light-years per decade. Intrepid-class starships like Voyager are faster than Galaxy-class starships, with Voyager's maximum sustainable speed being warp factor 9.975 and the Enterprise-D's being warp factor 9.6; so, with the Enterprise-D only being in service for three years as of this episode, there is no way it has more than 10,000 light-years of travel on it. In fact it likely has less than 3,000 light-years on it.
La Forge says that he is going to shut everything off and use only two thrusters. Picard actually uses three: starboard, port, and starboard aft.
Geordi states that the Enterprise has tens of thousands of light-years on it. Distance traveled has little meaning for ships and aircraft as wind and currents can greatly affect how far they go in a given time. It is therefore more accurate to use time units (usually hours) for a measure of how long the ship has operated. This would be especially true of a star ship that warps space to move "faster" than light.
When La Forge investigates how to get out of the booby trap, he runs across Dr. Leah Brahms' name and says "Who is this?" It would be unusual for La Forge, a chief engineer and a Star Fleet Academy graduate, not to have studied the person who wrote the book on warp propulsion.
After O'Brien transports the captain and others to the Promellian ship, he and Riker have a brief dialog just before there's a slight power fade. Riker doesn't check on the away team to make sure they are OK. He just leaves.
Just before the Enterprise begins its escape from the asteroid field, the computer is (annoyingly) making announcements about the lethal radiation exposure. Riker orders the computer to discontinue the radiation alerts "until further notice." Why does Riker say, "until further notice?" The ship's computer is great, but doesn't have a mind of its own - or does it? Once Riker orders the computer to discontinue the radiation warnings, that should be adequate, shouldn't it? Unless Riker is concerned that the computer might arbitrarily begin the radiation announcements on its own? "Until further notice" is definitely a phrase we say to humans (or sentient beings in the Trek universe) but not usually to computers. It should be that the computer will never again issue radiation announcements until told otherwise.