So we had (since today) one WP installation on 3.2.1 (I updated this one as well) and two others with the latest 3.4.2. All were/are working with WP Super Cache and Social and we have no problems at all.
You should take a closer look at your WP Super Cache options and check if there may be some that can contradict the behaviour. Do you use debug mode or logging or something like this? Legacy mode... You should check if one of the options you have activated causes this error.
Another thing you can do, just as a workaround though. When you open the social.php and go to line 356 it reads:
Social::$log = Social_Log::factory();
I don't know exactly but I guess what this does is start some kind of logging. So you could try and outcomment this line with two Slashes like this:
//Social::$log = Social_Log::factory();
Then save the file an switch the WP CACHE defintion to true again.
P.S.: And yes maybe it only happens on multisite. For this reason it would have been nice of c3iq if he had told us if he uses multisite as well.