I'd demand a full demo down to the subfloor and studs with no less-than-perfect parts re-used anywhere. I'd also begin spouting specs of what the job should be like (you can learn those at the John Bridge Tile Forum) and tell him that you want every spec met or exceeded. Tell him that he gets just one more chance and not with the previous sub, and that you're going to be watching the whole process constantly taking pictures of it all. The contractor won't be a happy camper but if he's worth his salt he will agree to that since it is simply you asking that the job be done properly. If he balks, say thanks for dropping by, my lawyer will be in touch with you shortly.
There is no excuse for an uneven tile job or improper sloping, but if you selected the tiles and they are inconsistent in size, then you're stuck with the unequal grout lines which must now necessarily be there. Those can be spaced for best appearance which should come out looking acceptably well if not perfect. You can't do that by lining up one edge as is usually done, each tile will require adjustment. I've dealt with that headache before myself. The corners should all be straight and true on both sides and cut tiles should have the exposed cut edges eased over.
I have to wonder why the contractor didn't reject the tile job on his own- I sure would have and so would everybody else I know. That to me says this contractor isn't one to use and that you're probably going to be going to court over this. But give him one chance to make it right first and hopefully he will do that. I know I would.
Phil