As for the frequent complaints -- sure, the animation was occasionally dodgy, but I'd argue no less so than most TV cartoons of the seventies. There was a lot
of cutting corners in those days right across the board.
Indeed, while Filmation's animation (the actual movement of things) was about as limited and repetitive as it got in '70s cartoons, the quality of their artwork was above average for the period. Look at shows from their main competitor Hanna-Barbera in the same period and the animation and background paintings tended to be rather sloppier and rougher. Filmation shows may not have had much motion, but they looked good.
But in my estimation, TAS is just made of win. How could it not be? It's essentially 22 extra episodes of TOS complete with the original actors. I love the way Filmation put real attention to detail in, too. Oh sure, there are pink Tribbles and other occasional errors, but I love how for example the Enterprise fly-bys were done by actually taking stock footage from TOS and rotoscoping. Or that the interior sets of the Enterprise are basically identical to the ones seen in TOS. Little details mean a lot, and TAS really does strive to be faithful to its parent live action series for the most part. That it has been so neglected within the fandom for so long is regrettable.
Indeed. It was made by people who were big fans of the original show. And of course it was story-edited by D.C. Fontana, and about half its episodes were written by veterans of the original series (well, 10 if you limit it only to TOS writers, 12 if you include the ones written by Walter Koenig and TOS director Marc Daniels). It's as authentic a continuation as we could possibly have gotten in animation. The other studios that made proposals for an animated ST all wanted to add kid sidekicks and cute alien mascots and just generally turn it into a stock kids' cartoon. But the show we got, other than toning down the sex and violence, strove to tell the same kind of stories that TOS had told, albeit with unlimited freedom to create exotic aliens and settings.