"You're a dead man, Apgar! A dead man!" Ah, how I remember and cherish that line from when I first heard it 17 years ago. It sums up this episode perfectly, in which a comedy of errors (actually a tragedy, but it plays like a comedy, hence Data being an art critic for Picard's painting in the opening teaser) is remembered by those involved in the way they want to remember it. In what must've been a brilliant high-concept pitch by writer Ed Zuckerman, this episode is "Rashomon in the holodeck."
As Riker beams back from a space station after discussing the progress of a new technology ("Krieger waves," not to be confused with "Kegel exercises") being developed by scientist Dr. Apgar (Mark Margolis), the station explodes, killing Apgar. Riker is accused of murder by the local authorities (Craig Richard Nelson), and the extradition hearing is held on the holodeck, where witness depositions and the facts of the case are viewed like scenes from a play. This is a clever twist on the courtroom show, and the holodeck is, I must admit, the perfect venue for dramatizing this kind of fact-finding mission. The facts mostly surround a perceived attraction between Riker and Apgar's wife Manua (Gina Hecht), which in varying versions of testimony has Riker flirting with Manua or vice versa.
The Rashomon effect eventually plays like humor, where Apgar, in three different versions (1) takes a swing at Riker and misses and falls down, (2) receives two punches in the gut from a real bastard version of Riker, and (3) kicks Riker's ass (in the most unlikely of scenarios). This third version leads to the hilariously over-the-top "You're a dead man, Apgar!" line. Riker watches the simulation and buries his face in his hand.
Who really killed Apgar, and why? That's answered in a final act that nearly drowns in its excess. A lengthy scene of exposition threatens to collapse under its own weight. The technical role of the Krieger wave converter (and its implausibly perfect replication in the holodeck, such that it actually functions) is ridiculous, and requires pages of explanation dialog. But the plot is exceptionally tidy, tying up all loose ends, assuming you buy into the technobabble. I don't, really — but, dammit, I like this episode anyway. It follows the facts from beginning to end in the true, verbose spirit of TNG.