I've often thought that The Great Time War was Russell T Davies' best idea when he brought Doctor Who back to the screen in 2005. Although never a big believer in a consistent "canon", Who had acquired a lot of backstory along the way, which often counted against it when trying to tell new stories. For all we know, the Cartmel Masterplan may have turned out just great, but it was a symptom of a show talking to itself, not a wider audience, and you only have to watch the 1996 TV Movie to see how its dense, continuity and reference-heavy story crushes the spark of life right out of it. Whilst Davies and his successor Stephen Moffat are both clearly huge fans of the show, they're both populists, and the Time War allowed them to wave away any messy questions with "T'were Time War Wot Dunnit".
However as the series as wore on the Time War has had a couple of negative effects. Firstly, we don't get any other Time Lords or Gallifrey-set stories, which is a shame, because I rather like them, and the juxtaposition between the staid hierarchy there and the Doctor himself. A more serious consequence, however, has been the creation of a "hard line" between the old and new show delineated by genocide, and whilst I really, really don't want the show to collapse into some sort classic series Easter Egg hunt, it's been hard to not think that the new show is embarrassed by it's own legacy.
The Day of the Doctor is not, however, embarrassed by it's own legacy. Finally telling the story of the end of the Time War, and introducing the Doctor who fought it, it is not only trying to do everything I mentioned up in my first paragraph, but tie up a bunch of loose ends and set up some new dominos whilst it is doing so. Mostly what it does is link the Classic and Modern Eras with a story that wouldn't feel out of place in either, but with all the pizazz and explosions modern TV has to offer. I'll try and stay off the intricacies of the plot too much, although some spoilage is inevitable.
So, we have three doctors (well, in some senses maybe four, and in others all 13), the incumbent Eleventh Doctor, a returning David Tennant as 10, and John "Acting Legend" Hurt as the War Doctor. The story starts by zipping between the three of them, with 11 helping out UNIT with some odd paintings and 10 investigating Zygons and Elizabeth I, which also neatly ties up all the references to her during his run. The stories of 10 and 11 neatly intersect, and could happily make a two Doctor cross-over, but The War Doctor, mulling over the consequences of mass genocide via a Conscience of Mass Destruction, gets to see his own future, the men he will become.
As it traditional in these circumstances, the meeting of multiple Doctors is cue for a lot of bickering interaction between characters who aren't actually all the different. Hurt, in particular, is a joy, skewering the mannerisms of his younger/older selves, sounding for all the world like a "classic era" fan still disgruntled that the relaunch exists at all. Underneath it all is some neat character writing of how later Doctors has dealt with the scars of the Time War, and how it's changed them, which also has a nice meta-textual edge to it, before they all get together to solve the shows initial "running around fighting the Zygons" plot.
And then we get to solve the Time War. I think it's a nice way to resolve the impasse, to be honest, without invalidating the journeys of 9 and 10 (and to a lesser extent 11; the Man who Forgets) with their scars and guilt. The show hasn't had its history re-written, but it has had it's future freed. And in the midst of the final act, the show just sort of rolls over and becomes the warm tribute to itself that it has spent the previous hour trying very hard not to be. Everyone turns up to the save day, especially, after his refusal to be in the 20th Anniversery, Tom Baker, playing a far future Doctor/wierldy aged Fourth Doctor/completely different Time Lord/twinkly old scene stealing Ham/insert other theory here.
So the big questions. Does it hold up plotwise? Well, as much as any episode of Doctor Who ever does, pretty well unless you poke it too hard. Does it celebrate the show in all it's forms? Hell yes. Does the show look healthy heading towards year 51? Yes, I think it does, and poised to regenerate itself once again. So Happy Birthday Doctor Who, please keep changing.