Picard receives a threatening out-of-left-field message from DaiMon Bok (Lee Arenberg), the Ferengi whose son Picard killed many years ago while defending the USS Stargazer from an unprovoked attack (the details of which were recounted in the first season episode, "The Battle"). Bok says he will have his revenge upon Picard by finding and killing Picard's son. Except, wait: Picard doesn't have a son — or does he?
The man who might be Picard's son is Jason Vigo (Ken Olandt) the son of a woman Picard had a brief whirlwind affair with three decades ago before he shipped off to be in the lengthy employ of Starfleet. This woman, who has been dead for some time, Picard fully believes could have raised a son without feeling the need to inform the father that the son existed (on the account of her unconventional and independent personality). So now you can add to the list of Season Seven Family Tree Theater: Picard's heretofore unknown love child. "Bloodlines" also fits into the trend of these last few episodes by telling a storyline that feels appropriate for a series winding toward closure — in this case going all the way back to the first season to bring back Bok as sort of a bookend, (although it's an oddly obscure choice).
Picard sets out on a mission to find Jason before Bok does, because, son or not, Jason is at the very least a target who now needs to be protected. Picard "rescues" Jason by beaming him off a rock face while he's in the middle of a recreational climb (which provides narrative shorthand for his adventurous risk-taking personality). DNA tests confirm Picard's paternity, and Jason is none too thrilled to learn that his unknown father has suddenly been revealed and now hopes to be part of his life. The character meat of the story, which is neither bad nor great but is reasonably decent, documents the gradual acceptance of Picard that Jason is able to reach. Meanwhile, Picard finds new emotional possibilities in realizing he's a father when he'd long assumed that fork in the road had been bypassed.
The problem with "Bloodlines" is, of course, its completely implausible plot surrounding Bok's convoluted plan for vengeance. If you think about it at all, it makes very little sense, especially once it's revealed that Picard's paternity was faked by Bok himself (who manipulated Jason's DNA) in order to concoct the "vengeance upon the child" scenario in the first place. I'm not an expert when it comes to blood-for-blood revenge, but somehow the idea of staging the creation of your enemy's son, then threatening to kill him, and then killing him (which Bok fails at, but let's suppose he had succeeded) seems like a really roundabout and, well, ineffective way of achieving satisfying revenge.
The final showdown between Bok and Picard has no juice (and lots of exposition), because Bok is so strategically outmatched and pathetic that it's hard to picture any legitimate menace here at all. Really, "Bloodlines" contains this plot only because it has to have something for the audience to latch onto besides some character moments that cannot carry the hour on their own, while building in a reset that undoes the notion of Picard actually having a son. The whole thing plays like a compromise.