I have finally finished LoTV, and uninstalled the game immediately after.
Gameplay-wise, I think the campaign was fine, and did its best to keep the player on their toes. I did get tired of the whole "kill/conquer/secure N objects/places/monsters" formula that is every mission, but that's the standard with Blizzard these days, and the as mechanics in the missions themselves did vary and were unique, I'd say they did a decent job with mission design.
The plot, on the other hand...
Story spoilers follow. You've been warned.
Remember how I said the campaign started off fine? Well, it did... But quickly degenerated into a walking pile of cliche towards the end, with the Protoss screaming "FREEEDOOOMMM!!!!!" and me wondering how this group of xenophobic, genocidal "Others" could, under Artanis's leadership, become the equivalent of Mel Gibson's Scots in the space of two expansions. It is difficult to separate the Protoss, at the end of the Legacy of the Void, from any generic group of idealized protagonists fighting for freedom against oppression and that, to me, is the actual Legacy of Chris Metzen's Void. The way the Protoss ended, they're basically no longer Protoss, but just another group of peace-loving humans who's liable to get rid of the caste system and establish democracy.
The "Kerrigan, the Lifetime Show Finale" that is the epilogue is full of ridiculous plot developments. Sure, it wrapped up the story line between Raynor and Kerrigan, but at the same time, it also cemented that story line as the center piece melodrama of Starcraft II, thereby showing that, in the end, Starcraft II was just a round-about way for Kerrigan and Raynor to get back together. The amount of cringe-worthy idiocy in Amon being a giant space god is topped only by Tassadar being another giant space god, which then completely undermines his sacrifice in the original Starcraft as it was just another act in his eternal war against Amon. It also makes his second sacrifice to make Kerrigan a naked space woman all the less moving because it was done in the space of seconds after discovering he was "still alive..."
The new characters were all forgettable stock characters, with the single exception of Alarak who is decently presented as a ruthless douchebag, but still just as cliche.
All in all, Legacy of the Void ends Starcraft II the way it ought to have begun: having never been made.