One item was dropped in the garden room by shift-clicking it in my inventory. When I opened the inventory, there was nothing on the floor. Just vanished. I even turned clipping off and walked through the floor to see if it was underneath, but nothing was there.

The second has just happened in the Vault area. A sword was dropped because I was encumbered. I saw it on the ground, went to another chest to unload stuff, came back and it is nowhere to be found.

This hasn't happened anywhere else, just in Frostcrag.

What version is your game?

I've installed the official updates and unofficial updates from the start. (sorry I meant to include that in the first post)

That's a bit vague.

To be more specific, do you have the 1.2.0416 patch installed?

Yes, that patch, the unofficial oblivion patch, the frostcrag esp and the unofficial frostcrag patch.