Was only slightly noticeable early game, got really obvious by lategame.

Our team, Shen Blitz Amumu LB Caitlyn, would use various CCs, and while most of them would land properly, every so often Diana would simply not be affected by it.

Not sure how to reproduce, however one thing to note was that she had two Tenacity Items: Merc Treads and The Jungler Spirit Item. Other than that, I don't know.

Shield protects from spells?

Her shield may have had something to do with it, not sure. Anyway, she would do things like be perfectly mobile while being knocked in the air so I don't think it was intended.. It was pretty surreal.

Her shield is health only.
That sounds like a really bad bug. If you could look under your "Recently Played" in your friends list, you can find your opponents. If you click on their profile, you can see their build for that game. If you can report their build (or even better, predict the runes and masteries they used) that all helps the Q/A reproduce the bug to narrow it down.

Unfortunately I'm 4000 in Queue to get in PBE. I'll update this when I can.

Well it is probably too late unless you remember his username. That recently played list gets cleared when you logout...

You can also find details of your latest match in your r3d log.

Oh, good idea. From there we can get the opponent's username?

There's also that new Mastery that further increases Tenacity by 15% in the Defense tree, as well as the Slow reduction Mastery there too.

Combine that with a Tenacity item in-game and it should be rather difficult to keep that Champion CC'd for very long, as that's pretty much a straight 50% reduction in CC time. I think the slow reduction Mastery stacks on top of Tenacity as well so you're looking at around a 65% reduction in slow times (maybe less since it probably stacks multiplicatively instead of additively).

Yes, and I can post my r3d log as an example if necessary.

Tenacity does not affect displacement CC. If Diana can walk whilst in the air knocked up by Blitzcrank, which is how I interpret it, then it's a serious bug.