The scratches are permanent unless you want to get into refinishing. For the discoloration near the wall, I'd be tempted to just cover it with a some sort of simple wood corner molding.

This looks very much like the veneer cabinets I have where the veneer came off with painter's tape. I had put the tape on to protect the finish from some floor work I was doing, and presto, I had a big problem. I ended up finding some stain to match my cabinets (got lucky) and fortunately, the tape was low on the cabinets, so I just trimmed out the bases with some 4 X 1/4" stained poplar. Looks nice, no more eyesore.

Though your issue is not at the base of your cabinets, I mention this only as a potential alternative. With a solid wood, you could ease the visible edges of it to make it bullnose attractively into the cabinet side.

If you did it right, you could make it look like it was designed that way all along!