In some ways, it's really hard to appreciate "Encounter at Farpoint." As with the majority of the first season of Next Generation there's an aesthetic that was outdated even upon original airing, indicated by the dramatic shift in quality beginning with the third season (although even the second season was markedly better if less distinguished). The main crux of the episode, the crisis at Farpoint as Picard struggles to learn what exactly is going on (not the only parallel with the series finale "All Good Things..."), is hardly worth watching for the most part, much less commenting on. We do get introductions to each of the characters of the series, however, including Data's memorable whistling of "Pop! Goes the Weasel" (which is what Riker struggles to remember in Nemesis, by the way, even though he's the one who finishes the tune, though you may be forgiven if all you yourself remember is that the scene is also the introduction of the holodeck).
The real meat of the episode was actually included as an afterthought, once Paramount decided to make "Encounter" a two-hour affair. That meat would be Q, as memorably portrayed by John de Lancie, who perhaps is the greatest bit of continuity through the rest of the series and several others besides. If anyone but de Lancie had been cast, Q would very easily have become just another of Star Trek's meddling omnipotent beings, another link fans just getting into the first new Star Trek cast since Kirk would have scoffed at seeing again (this would be a problem in other first season episodes).
Also memorable but not as striking is DeForest Kelley's cameo appearance as an aged "Bones" McCoy, buried under so much bad prosthetic makeup (another episode from the season would feature bad prosthetic makeup, in case you were wondering, "Too Short a Season") that even his distinctive voice might be hard to catch. He takes a short stroll with Data (making the android easily the other character, besides Q, to make a definite impression from "Farpoint"), touring the new Enterprise. If you didn't know it was Kelley, you certainly wouldn't know it was supposed to be McCoy. Kelley would leave better impressions in The Final Frontier and The Undiscovered Country, both released after this pilot, though this is his final TV appearance.
For those looking for niftier continuity casting, this is Colm Meaney's first appearance in the franchise, though his character (Miles O'Brien) doesn't receive a name. It took a long time to establish a character for Meaney, but he eventually became a regular, in Deep Space Nine.
In other tech developments, the Enterprise performs a rare saucer separation, which may be another notable aspect of the episode worth watching. It's the odd bits, not the entirety of it, that makes "Encounter" its own kind of new Star Trek classic, not just because it makes history in itself, but because there are definitely things worth remembering and savoring.
But mostly it's Q, not Jean-Luc Picard, who gets to see what's out there.
franchise * series * essential * character
John de Lancie
Memory Alpha summary.