In the Refined Storage Disk Drive, in which you can see the armor slots appearing correctly, there is a button for "Priority". Pressing this button reveals a second GUI where the slots appear again, but misplaced this time.
http://i.imgur.com/xPhR0nD.png

Wearing any armor, if I try to shift-click any of it off, the game will crash, producing this log -
http://pastebin.com/pSdztEyf

Clicking normally on the items works, but shift-clicking will crash the game. This GUI technically isn't even an inventory, so the armor slots probably should not appear here to begin with.

I see that the mod is now compatible with any container, but most containers have this strange offset between the armor/icons and the grid that is supposed to be directly behind them. They also appear in poor locations at times.

Some "inventories" where the armor slots appear in a bad place -
http://i.imgur.com/IaLcQ42.png
The RFTools Control Programmer

Some blocks with UIs where the armor slots shouldn't be appearing at all -

http://i.imgur.com/XyIZvfE.png
The RFTools Timer, Sequencer, Logic Gate, and more.

http://i.imgur.com/OLdI3wa.png
EnderIO Capacitor Banks (doubled)

And even beyond that, the Refined Storage Grid has the armor slot GUI appear, but the slots are not actually accessible.
http://i.imgur.com/YE98k3g.png
Despite appearing, the bottom left inventory slots for armor cannot be used, and the armor currently equipped cannot be seen.

I really do appreciate the appearance of the armor slots in inventories like iron chests, so I'm hoping the few remaining issues can be ironed out. Thanks!

Thanks for the details, I'm almost done with the new version that should fix all position/alignment issues.

I haven't considered UI's that don't have slots, I'll add that to my to-do list before release.

Is there any chance of a backport of the fixes to 1.10?

Yes, a 1.10 backport of the latest version is already on the way. I finished most of the code changes, now I need to manually test with some modpacks and fix any issues I find.