What I expected to happen was...:
Armor overlay gets removed from player after taking of armor

What actually happened was...:
Armor was sill visible to OTHER players, not the player itself.

Steps to Reproduce:
1. Get 2 Players
2. Equip armor with 1st player
3. Remove Armor by pressing "Q" while hovering over the armor slots with the mouse
4. Close inventory by pressing ESC! IMPORTANT (Other closing options won't work)
5. OTHER players will still see the armor, although the player has taken it off. (Gets fixed by pressing "E")

AFTER STEP 4: If the 1st player has an Armor part in his hotbar and right clicks it, it will equip and the OTHER players will still see the item in his hand, although he used it.

Attachment: Video "Proof" on 1.10 local server with Vanilla Premium Accounts