There are several elements to this story that not only make it great - but even make it a bit beautiful:
The first and most obvious one is the character of Tommy. Although we're never told why a person with special needs is allowed to roam freely about a monastery (and, from an extremely budhist point-of-view, it's almost sort of nice that it's never explained), his involvement in this story is crucial to its noteworthiness. As a viewer, I grew attached to Tommy in ways that I never have before in a Doctor Who story and, for that matter, never have since. I like him quite a bit already even before the Blue Crystal changes him, but as I journey with him after the change I, pretty well, fall in love with his character. So that when he finally dives in the way of the blast of mental energy in the basement, my fear for his safety caused me to produce an audible yelp. Amusingly enough, others who have watched this story with me had a similar reaction to that moment. Which just goes to show, really.
Another really downright fantastic element of this story is K'anpo/Cho-je. At last, we meet this mysterious mentor of the Doctor's. Even though we only ever heard of him for the first time a season or two ago - we were immediately fascinated with him. And it's almost a bit sad that he does get referenced one or two more times in the series, but we never do actually see him again. Still, the meeting they have near the end of the story is completely worth stopping the whole plot for. It's a magnificiently scripted and performed scene. And the ultra-cool regeneration that follows as K'anpo morphs into Cho-je almost "steals the the thunder" of the Doctor's regeneration.
Almost, but not quite.
The strongest, most powerful, element of this story is the demise of the Third Doctor. Written in a way that is still quite grandiose (after all, Pertwee did carry the role for five years and deserved a noteworthy swansong) without being quite so intentional about it as "Logopolis" was. The grandness, in fact, is executed in what I feel is the "right" kind of way: through some really strong characterisation. The Doctor, because of the nature of his character, is frequently a "constant" in his stories. With little or no real sense of growth to him. But the journey he takes in this tale leaves him a changed man by its conclusion. And not just in a literal sense. And though there have been other stories where the Doctor had brief "snippets" of character growth (ie: the little moment in "Ressurection of the Daleks" after Tegan leaves where he feels he "must mend his ways") - this story really makes the Doctor's character growth its most pivotal point. And this is what really causes the whole story to shine. So that, as he collapses to the floor of the UNIT lab and bids his adieu - I am truly touched by his departure. It is, in my opinion, some of the most compelling drama of the Pertwee era. Thus making it the best note for the lead actor to leave on.
As has been discussed in other reviews, Planet Of Spiders has some very "clunky" moments to it too. If there's any evidence that the show was getting too dominated by Pertwee's personality, it's the chase scene. Purely a twenty-minute throwaway that becomes difficult to watch after seven minutes or so. It does almost seem like they're just completely indulging Pertwee's love of strange vehicles. But it does have, at least, some fun little comical moments to it involving the police officer and the sleeping bum. And even the Whomobile flying is kind of a neat twist. Even as fake as it may have looked. So, as bothersome as the chase sequence might have been, in some ways, it's still not as bad as all that.
I'm probably more bothered by the apparent "woodeness" of the cast of villagers on Metebellis Three. Wow, there's just some really bad acting going on in some of those scenes. Most cringeworthy of them all is the woman who played the mother. I'm sure she was cast because she was related to the right person. No one could have been impressed with her as an actress! The fact that she really painfully flubs one of her lines just makes matters worse. Easilly, one of the worst performances ever done in a Who-story - and there have been some bad ones over the years! But, if given the choice of going back in time and being able to alter only one facet of this story - it would be the re-casting of this character before it would be taking out of the chase scene.
There are probably a few more weaknesses to this story but the strengths, I feel, definitely outweigh them to the point of making them painfully irrelevant, for the most part. The story shows some very strong continuity with the way it wraps up a few important ongoing threads that have been weaving through the series. One of particular noteworthiness was the final progression of Mike Yates. Ever since "Green Death", the series seemed to be doing some interesting things to him. Which I felt was a great move. Compared to the Brig and Benton, Mike was painfully bland in most of his stories. To take him through the journey they did was a nice touch.
Another really nice touch was the fact that, although the story celebrates many of the quintessential aspects of Pertwee's era, it also strays from it in other vital ways. Thus giving the whole thing a bit of a "Caves Of Androzani" kind of feel. Like that story, things happen in Planet of Spiders that don't normally happen in the Third Doctor's tenure. And that aspect, in itself, makes the story all the more enjoyable. Particularly to someone who found much of this era just a tad too formulaic for his liking.
So, the final verdict is that the story does have its fair share of flaws. But it also "transcends" (you can't help but use that word in a story about Budhism) a lot of the restrictions the series imposed upon itself at the time. And that, more than anything, is what makes Pertwee's farewell both memorable and even a bit beautiful. A very deftly-crafted sentimentalism that could have been easily messed up in less-capable hands.