Do a google groups archive search here as the APEX schematic link has
been posted many times. "apex service" finds this useful post in under
3 seconds:

http://groups.google.com/groups?q=ap...gle.com&rnum=2

There are no common problems, Apex stuff is cheaply made with cheapest
parts.
I guess if you consider solder connection problems common, they have
lots of them.

The tv is simply to cheap to ever have repaired, so unlikely anyone has
really ever worked on enough of them to even have an idea of a common
problem.