Encounter at Farpoint

• Picard and Dr. Crusher have a history, and Picard may have been involved with the death of Dr. Crusher's husband.
• Riker is Troi's imzadi, a relationship which involves psychic or empathic communication.
• Worf has issues about Klingon honor but generally obeys orders.
• Worf is quick to point a phaser at the viewscreen when Q shows up onscreen, making him both quick on the draw and slow to think out the consequences of his actions. (Thanks to eien_meru for pointing out that this was Worf and not Tasha Yar.)
• Wesley Crusher is, and always has been, an annoying little shit.

Plot:
(minor spoilers)

The new Galaxy-class USS Enterprise (NCC-1701-D) is en route to Farpoint Station to learn how they were able to build such a great station so quickly on a planet with lots of geothermal energy but few other resources.

A mysterious energy field traps the Enterprise (we haven't seen that before, now have we?) and Q beams himself aboard dressed as a post-Renaissance explorer, possibly Christopher Columbus, with a wacky Amish raft of thee and thou-ery.

Q says that humans are a savage race, always have been, always will be. Picard suggests that Q judge humanity not on its past but on how it behaves now. Q is delighted by the suggestion and promises that the mystery of Farpoint Station will be a challenge that will demonstrate what humanity has become.

In the end, Q reluctantly agrees that humanity is better than it once was. He has taken to calling Picard "mon capitaine" ("my captain"), which I suppose counts as character development for omnipotent characters. Just before the credits roll, Picard promises that their future adventures won't be like this one -- they'll be much more interesting.