I've been playing through co-op on Steam with a friend. Here are the things that we've been encountering:

-Health bars on the left side of the HUD sometimes display as not full health for the non-hosting player, when in actuality they are full
-Status effects, debuffs, and skill cooldowns often do not countdown until complete, i.e. stun will show 2 turns until it's gone, rather than 2->1->gone. Skill cooldowns will show how many turns left if moused over, but the ticking shader will often be incorrect.
-Turn order at the top of the battle HUD will frequently get stuck, and misrepresent actual HP bar values.
-Skill bar at the bottom of the HUD sometimes disappears for the non-hosting player. Reappears after a save/reload.
-This has only happened once so far, but ALL skill AP costs were inexplicable increased for the non-hosting player. Most were increased by 2; Farseer was a particular offender, going from a cost of 2 to a cost of 6. Persisted after battle. Fixed upon save/reload.