Hi there, I just did a fresh install of Mountain Lion 10.8.5 on my unsupported MacBook4,1 using NexPostFacto, and also discovered that App Store seems to be broken. This was also the case in Lion 10.7.5 before I upgraded too I noted. To get around this, I opened up terminal, and typed:
sudo softwareupdate -l
to list all the updates available; and then used commands like:
sudo softwareupdate -i SecUpd2015-006MtLion-1.0
to install all the updates, one at a time using each entry as listed via the first command.
The odd update had spaces in the name. In this case, I used 'random package name with spaces' around the necessary updates. So in example:
sudo softwareupdate -i 'Mac App Store Update-1.0' -v
The only update I could not get to install was iTunesX-12.4.3 using this method. Hopefully this helps someone.