The computer twice reports the location of Alexander. But Alexander is not wearing a comm badge, which is how the computer keeps track of where anyone is. However, that is the primary method. The computer can use internal sensors to track life-signs. Distinguishing different adult humans is presumably more difficult, which is why comm badge signals are used. On the other hand, finding the one Klingon child on board would be fairly easy.
In the holodeck scene, Worf orders the computer to "freeze program". Yet the smoke behind him as well as the ground fog around Alexander still continue to move.
When Alexander has the field trip and stands next to the Gilbos terrarium, his head and shoulders can be seen on level with the creature. In the next scene he is barely able to look in the cage at all.
If the speed of the wave increased unexpectedly, it should have missed the target planet due to planetary motions.
After the test ship riding the Soliton wave is destroyed, the wave begins to significantly increase its velocity (thus its energy) and size. However, how the wave has increased in energy is never explained.
Kahless is pronounced here as "Kah-less" while all other Trek productions about this character call him "Kay-less".
When the senior officers enter the bridge after the initial briefing on the Soliton Wave by Dr Ja'Dar, Deanna, speaking to Worf about Alexander's teacher, should have referred to MISS Kyle rather than MRS Kyle.