On the bridge, when Wesley, Data and Geordi explain the source of the radiation to Picard, Wesley's hair style significantly changes from the wide shot to the close-up.
The female art student paints while resting the back of her little finger directly on the canvas, indicating that the paint is totally dry. This would not happen in such a setting as the requirements of a live model maintaining the same exact pose would mean that the entire painting would need to be done on the spot without drying and multiple sessions. If she had been doing it for real, she would have been using a Mahl stick to support her painting hand.
Oil paints do take a long time to dry. However, if they had been using acrylics, the paints could easily dry during the course of the session. (Moreover, some future development in paint technology could lead to quick-drying oil paints.)
In Manua's version of events, Riker paraphrases the story of Rapunzel. There is no reason to think she would know an Earth fairy tale. **No reason to think she wouldn't, either; why not?**
When the holodeck program is paused during the third version of events, the computer lights continue to blink.
When Geordi first brings up his simulation and is walking through its function, the "frozen" holographic images of Riker and the others can be seen moving slightly, indicating that the actors were just trying to stand very still, rather than images of them being paused.
When Riker is walking through the frozen holographic recreation of himself and Manua, the "real" Riker is very blurry.
The image of the planet is obviously of a textured surface slowly moving beneath a mask and is clearly not spherical.
At around 22:16, after Manua Apgar entered the holo deck, the sound of the closing holodeck door comes from the right, though according to the picture, it should be located in the center.
Krag points to the sensor logs that show an energy discharge from Riker's position to the science station's generator. Krag claims that Riker fired a phaser just as he beamed out. No one disputes this. But in The Most Toys (1990) O'Brien can tell that a phaser has been fired just before transport. Surely he could read Riker's weapon as well, and that would be evidence as to whether Riker fired at all.
Riker is accused of firing a phaser just as he was transporting. But when he materializes on the Enterprise he isn't holding a phaser and there is none on his belt. O'Brien could have testified to that fact.
One of the minor points in dispute is where Riker and La Forge planned to spend the night; Mrs. Apgar's testimony indicates that Riker invited himself as a guest on the station. Riker's testimony, however, indicates that he had already made arrangements for planetside accommodations, and a record of such arrangements should exist.
With Riker and LaForge being on a mission to get an update on Apgar's work, there would have been no reason for them to have carried phasers.
When Tayna concludes her testimony, she mispronounces Manua's name.