In comparison to the other stories involving the Doctor on Gallifrey, this one is the weakest of them all. And that's probably what causes it to leave such a bitter taste in most of fandomn's mouth. But if we view this story on its own merits, it's really not so bad.
It's got a decent little plot structure to it. Two different events at very different locations eventually entwine in a somewhat clever way. Very stereotypical Davison era-type stuff. It's got an old villain coming back with a new twist to him. It's even got a nice foreign location that doesn't actually slow down the plot too much in order to show off that the crew went to a foreign location (sorry folks, but some of those scenes in "City Of Death" of walking and/or running through Paris could've stood a bit of trimming!). It's got quite a few nice things going for it. So why, then, does "Arc of Infinity" get panned as much as it does?
For me, the biggest problem of this story is the techno-babble. There's just a bit too much of it, really. With barely enough explanation given to what all the babble actually means. For instance, we have all these vague references to molecular bonding with the Doctor. It almost sort of happens in Part One. It's what keeps the Doctor alive through Part Three. But then, suddenly, in Part Four, Omega just seems to do it all on his own. How exactly does that work? I suppose, with a bit of imagination, one could theorise that the bonding process needs the Doctor alive as a sort of "master copy" for Omega to work from. But it's never properly explained. And, though there have been some other stories where ideas where not given full explanations (ie: "Warriors Gate" or "Ghost Light"), this seems to come across more as lazy writing than creative effort. Now add to this seven or eight other "techno-babblic" ideas being thrown out all over the place and we really find ourselves wondering if perhaps Johnny Byrne just didn't feel like getting bogged down with too much of a real plot. And that, everytime he got stuck, he just came up with a pseudo-science of some sort in order to work around the problem. The "pulse loop" in episode four being a great example of this. We get the vaguest idea of how it works. But it really should have just been called "A piece of techno-babble I made up in order to get the Doctor off Gallifrey without Omega knowing". It would have been just as effective of a name.
This problem persists throughout the story. No proper explanations get offered anywhere, really. How exactly did Omega gain control of the Matrix? Or the Arc of Infinity, for that matter? How was Hedin able to use Borussa's code to get the Doctor's bio-data extract? Again, we can fill in the gaps using our imaginations but when I find myself doing that as much as I do in this story, I can't help but think that maybe the writing is a bit weak instead. And this remains my biggest problem with this tale.
Some weaker, more "niggly" negative points would be Gallifrey's new sense of interior design. Personally, I loved the way things looked in "Deadly Assassin" and "Invasion of Time" and though I can appreciate a need to "re-vamp" things slightly, they went a bit too far and made the interiors look far too radically different from what they used to look like. It's a minor point, I know. But it always "puts me off a bit" when I watch this story.
My other minor complaint would be Borussa. In this incarnation, he doesn't seem at all like any of his predecessors or his successor. Is this the fault of the writing or the directing or the acting? I can't be sure. But, to me, this just doesn't seem like the Borussa we've seen before or after. Might have been better to just have an entirely different Lord President and have Borussa still on council. I know this could work to the detriment of "The Five Doctors" but it would have made it a bit easier, I think, for the fans to digest in this story. This just doesn't seem like the Borussa we know. Although, at least, his harsh decision to kill the Doctor heralds his growing sense of corruption. So, it's a bit of foreshadowing, I suppose. Mind you, I doubt this was done intentionally.
Now, before I go too far into the criticism, there are some things about this story I like. Part Four is an especially strong episode. Yes, the chase scenes are somewhat gratuitous and show off the Amsterdam scenery quite a bit. But, at least, it remains an interesting chase. Different things happen along the way to keep us involved. Had it just been shot after shot of Omega running down a street and then the Doctor and his companions running down the same street a moment later, I would feel entirely different on the matter. But with all the different incidents happening along the way, the sequence seems justified. And even quite enjoyable. And, of course, Omega's stop at the organ grinder is very touching. Much praise has been given already to Davison for his portrayal of this moment, I'll heap on some more. It really seems as though this is not the same man we see chasing along after himself a moment later. And, though Doctor Five is not quite my favourite, I do consider Peter Davison to be probably the most talented actor to have taken on the role. And this moment is one of the more shining examples of his talent. Though there are many more...
The character of Omega, himself, is another really great strength to this story. Changing his appearance was not just good for plot expediency, it was very symbolic of who he had become. The ranting maniac of "The Three Doctors" was still buried deep within the character. But the tragic element of his tragic hero personality was played up one hundred percent. We almost can't really call him a villain. He's just a man who has become consumed with trying to get back home. And the obcession has made him so unreasonable that he's willing to abandon any morals he may have once had. The "poor unfortunate wretch" dialogue that's spoken after he passes on is truly befitting of our sentiment for him. We're glad to see the world saved but sad to see how the man threatening it was sacrificed. An excellent sense of pathos. I loved it.
Overall, this story rises just a bit above mediocre - but not much. Which is another thing that works so much against it when you view it in context of the rest of this series. Not only is the weakest of all the "Gallifrey-bound" stories, but it was also the opener for the 20th anniversary season. And it causes the season to start off with a fizzle rather than a bang. Still, as I said before, view it on its own merits and it's not so bad. Even quite good, in places!