I can get items to save if I unlock on the main screen and EQUIP them, then jump back to single player and then jump back to multiplayer. My weapon unlocks have now saved.
I am still having issues with dog tags and my level, it cant seem to remember what dog tags I had and what I just unlocked. It also has problems telling me my level, it either tells me I'm a level above on the main multiplayer menu or when in-game it tells me I'm actually a level below.