Any normally-enchantable gear can be enchanted at the Enchanting table with no problem.

However, issues start to take place with Enchanted Books. Whenever an item (enchanted or not) is used at the Anvil with an Enchanted Book, it will cause the item to seem enchanted, take away experience, but then "rubber band" the item and book back to your inventory, minus the levels consumed. This process cannot be repeated unless the anvil is interacted with again.

Levels restore if logging in and out again.

This pattern can be temporarily bypassed by enchanting a NON-ENCHANTED item with a single enchantment on a single book. If the book has multiple enchantments on it, this will fail, repeating the previously-mentioned pattern. If the item is previously-enchanted, and a single-enchant book is used, this process will fail as well. It seems that, as long as single enchantments are put on a fresh item, one by one, this has LIMITED success; however

Mending seems to have to be put on an item first, and sometimes this causes the client to crash. If client crashes in this fashion, the item and book seem to be lost.

Edit: I found out how to get this to work more routinely:

Step 1: Make sure the item has no enchantments on it.
Step 2: Enchant the item at the enchanting table.
Step 3: Strip all enchantments from item on the Grindstone
Step 4: You may enchant the item with books, one enchantment at a time. Books with multiple enchantments may crash game.

Is there a crash-report for the mending one?

I haven't uploaded it, yet. I can see about finding it and posting it.
Edit: Posted crash report