Picard is painting nude womens! Data performs some art criticism of the students' work and is somewhat scathing of Picard's attempt. Ah, humour.
They beam Riker off a space station as it explodes. He's somewhat surprised when O'Brien informs him the station just blew up. According to Riker, the only other person aboard the station was Dr. Apgar. Chief Investigator Krag of the local security forces comes aboard and announces he's taking Riker into custody on suspicion of murder.
Krag says under his civilisation's law system, suspects are guilty until proven innocent (wow, harsh! They must have lots of innocent people in their prisons). Picard insists the trial occurs on the ship, since they don't have the budget this episode for new sets. They'll use the holodeck to recreate what happened on the station.
18 hours later, Picard, Krag, Riker and Troi walk onto the holodeck recreation of the station. Riker says he was there to look at a kreiger radiation converter. They replay Riker arriving on the station, and observe Apgar's wife giving Riker a good eying up. Though he says he and Geordi have accommodation arranged on the planet, Manua insists they stay on the station. And then makes sexual advances on him. Apgar, of course, walks in on them and gets the wrong idea. The next morning, Apgar yells at him, and he transports off.
Krag asks about the firing of a phaser, which Riker denies happening - Krag says that a phaser was fired just as Riker beamed off, and it came from where Riker was standing. Krag plays his version of simulation, which has Riker firing off a phaser right as the transport kicked in.
This is quite obviously wrong, since as we already saw, Riker arrived on the Enterprise in a neutral pose with his phaser in its holster.
Geordi, Data and Wesley puzzle over the sensor data, then there's a radiation surge on one of the Enterprise's decks which melts a wall panel.
Manua Apgar is brought on board the ship to present her side of the story. Which shows Riker as the one who was making sexual advances on her. Quelle surprise. I'm going to hazard a guess here and suggest that Manua was having an affair with Apgar's assistant. Riker protests strongly at this testimony, but they resume the program and watch simRiker beating on Dr Apgar.
Troi says she didn't sense any deception from Manua but still trusts Riker. Real helpful there.
Crusher has to evacuate sickbay because of another mysterious radiation buildup. Data quickly notices that the radiation events are happening at precise intervals, and the station explosion matches up with one of those intervals.
Tanya, Apgar's assistant, gives her testimony as related to her by Apgar himself, describing how he found Riker and Manua kissing, and then punched out Riker. HAHAHAHAHAHAHAHAHA! Doesn't Krag find it suspicious that no two people agreed on what happened? At least two people are obviously lying.
Picard anguishes that he'll have to allow Riker's extradition, but Data and co report that the recurrence period of the radiation is the same as that of the planet-side generator that Apgar was using to power the station.
Picard revisits the evidence, and suggests that Apgar had already created Kreiger waves, and the holographic converter is using the power from the generator to create Kreiger waves. Apgar wouldn't get any profit if the Federation got control of his work. Apgar tried to use the generator to kill Riker, but the discharge bounced back and destroyed the station. A simulation is played back and successfully convinces Krag of Riker's innocence. Riker is relieved. The end.