The Enterprise arrives to open diplomatic relations with the bifurcated world of Kesprytt, which has petitioned for entry into the Federation. Correction: The Kes have applied for Federation membership; the isolated Prytt have not made any such request and, indeed, apparently do not even talk with the Kes government with which they share a planet. Picard and Crusher beam down to the planet to meet a Kes delegation but are intercepted by the Prytt and thrown into a holding cell and accused of being Kes spies. The Prytt install brain implants that are ostensibly used to obtain truthful information from the prisoners, but which have the side effect of telepathically linking Picard and Crusher so they can hear each other's thoughts.
From here emerges two story strands connecting the overall premise: Picard and Crusher escape their holding cell (with the help of some covert Kes operatives) and must deal with the consequences of being joined at the hip (the device doesn't allow them to move more than a few feet from each other) and privy to each other's thoughts, while Riker aboard the Enterprise attempts to open communications with the Prytt to negotiate their release. Riker does this with the help of Kes Ambassador Mauric (Robin Gammell), who offers such wonderfully useful insights as "We don't have any formal diplomatic relations with the Prytt."
Both of these stories work pretty well. What we have here is an effective and balanced episode of exploratory character work (Picard and Crusher), action-adventure (ditto), and a comedy of diplomatic frustration (Riker, Worf, and Mauric). While this is a story much more remembered (and rightly so) for its dialogue breaking down the previously unspoken history of Picard and Crusher, there's also plenty of entertainment to be found in the goings-on aboard the Enterprise, where Mauric reveals just how deeply the dysfunction runs on Kesprytt — and does so with a stunningly oblivious tone-deafness that borders on hilarious. For a world that wants Federation membership and should know to be on its best behavior, its utter failure via Mauric to put up a convincing front — even amid its deep divisions — speaks volumes.
This is played mostly for laughs of the situation's escalating frustration. Mauric is so paranoid of Kes spies that he insists on the highest of security for all discussions, and takes to combing through his quarters for listening devices. There's a running gag as his quarters fill up with big, flashy security scanners and gizmos that turn the room into what looks like a lab. The longer this goes on, the more and more absurdly paranoid Mauric becomes, until he's eventually accusing Riker of a labyrinthine scheme to join in an alliance with the Prytt.
Riker shows great restraint and professionalism in just continuing to even deal with the guy, but I got a good chuckle out of the scene where Mauric announces he's fed up and is leaving, and Riker says, good, and "Make sure you take all this junk with you." Even better is the scene where he lays out for Mauric and his Prytt counterpart exactly why he will be recommending Kesprytt be denied Federation membership. "Attached" may not be to Federation application scenarios as, say, "First Contact" was to first contact scenarios (which is to say definitive), but it does show one such scenario with a decent dose of entertainment value.
The emotional center of the episode is, of course, Picard and Crusher, and how the devices that have connected their thoughts now force them to say things that for many years have gone unsaid. While some of the early I-can-read-your-mind one-liners come across as obvious and hackneyed, the lengthy fireside discussion where Picard reveals that he was at one time, long ago, in love with Crusher (while she was still married to his best friend, no less), strikes the right notes of honest, revealing, and reluctantly confessional. Naturally, you can rarely go wrong with a Patrick Stewart soliloquy, but the dialogue manages to meet the assignment of offering new insights into the characters without running the risk of making grand changes to the status quo. (This is like the long-delayed episode for 'shippers that is written with the restraint and depth that makes it feel organic, rather than like fanfic.)
And there's the story's final scene that manages to (sort of) have its cake and eat it too. I suppose it would be too much to ask that these confessions and feelings open up a new chapter in the relationship between Picard and Crusher (and Picard even floats it as a possibility); the story here is non-committal in its ambiguity. It manages to be satisfying by acknowledging that these two are more than just friends (and the performances are very good), but still plays it safe by maintaining the status quo. For TNG, even in its final season, that feels like an appropriate choice.