It appears as if Riker has murdered scientist Dr. Nel Apgar when the research station blows up just after he has transported away. The Tanugan investigator agrees to hear more of the witness' accounts before taking Riker in for a trial. This allows the crew to do their own investigation in an attempt to clear Riker. Following Tanugan laws, the witness testimony is used to create several holographic versions of events witnesses before the explosion. Riker's testimony and the widow's testimony are vastly different, yet both contain some of the same clues that eventually clear Riker. The research station appears to have blown up because the jealous Dr. Apgar attempted to shoot Riker, but the phaser beam bounced off of the transporter beam and into the fancy machine nearby. Actual dialogue and other facts are left unverified for the audience.
In other words, Riker may or may not have seduced and/or assaulted Ms. Dr. Apgar. It's tempting to be annoyed by the ambiguity, but in the end I find myself won over by the point that the episode was trying to make: witnesses remember the exact same events differently. We all see life through our own filters, and we go even further and edit our memories of the events after the fact. We don't even have to do it on purpose. Riker sees himself as a lady's man, and Dr. Apgar's wife sees herself as a loyal widow. The audience is left to assume that the truth lies somewhere in the middle. Riker was probably a little inappropriate, perhaps in response to a bit of innocent flirting. We've seen him flirt with plenty of other women, though we'd be disinclined to believe that he would kill in the name of jealousy. Unfortunately for Riker, the Tanugan people don't know him from Adam (or... Tanugan...?), so he's got to go through all that objective law stuff.
He'd better thank his lucky stars that Geordi's as smart as he is, and Picard as stubborn. If Picard can hold off Q, he can certainly hold off the Tanugan investigator. And Troi? she wasn't much help, except to let us know that all the witnesses were telling the "truth". In this case, if she had been of help, I would have been quite annoyed. She's an empath - she's not clairvoyant.
In conclusion, today's lesson is that I'm a sucker for correctly employed psychology.