In the inventory screen, you can mouse over an equipped item to get the expanded non-modal popup window of it. If you use the F1-F4 keys to switch to another character, the popup window does not refresh to the new character's item in that slot.

A similar issue happens if you mouse over a item in inventory - the popup window will show to compare it to the current equipped item, and that window does not refresh if you use the F1-F4 keys to switch heroes.