The client is very happy, that said. My personal concerns reflect your own.
-Guitar is too loud, not well defined
-Vox too low, not my preference, I'll sneak them back up a little. I usually mix vox too hot. Vocal harmonies were a contentious issue during vocal tracking. Others in the group had different ideas about what sounded right. I tended to agree with the vocalist on some of the major points.
-Bass is not defined enough, low mid tweaks are in order.
As far as monitoring at home, I actually mix at home (track in a studio) using 3 sets of monitors and two set of phones, but still have issues with translations. My room is treated, but still needs work.