Most sysadmins would argue that there are no "common" problems, however I would guess that 99% of problems deal with the user.
Most large corporations will break up the position of "systems administrator" and have specialties - just like in medicine - some people will work AD, some Exchange, some their flavor of Linux, some will deal with a certain web application, some will deal with Cisco routers, some will deal with other routers/switches, and a help desk that deals with the 99% of user problems. You'd have to ask each specialty what their most common problem is.