i played it coop years ago with a friend, it was very cool.
back then there was some problems with games becoming out of sync, i don't know if that still exists. i remember there was a problem with the quick load/save when you start a new coop game (after it crashed or sth) and we had to manually copy the quicksave file around to resume a mission, so we didnt have to restart from the start of the mission.
a non-technical "problem" is, that there are many parts in the game which can/must be solo-ed by the Green Beret or the Spy, so it might become a bit boring for other players. but afair you can change which player controls which commando during a session so you can take turns during those parts.
tl;dr version: besides some minor problems, the coop is highly enjoyable