Tonearm relative to Plinth alignment

No, there are 3 set screws so when they are screwed in, even loosely, you can't rotate it. Here is a picture so you can see:

http://128.121.219.98/i/c/f/1191460316.jpg

There would be no way to get it straight short of drilling new holes, so I was wondering if having it start at a few degrees rotation would affect the sound.

As long as your cartridge (cantilever) is properly aligned using a protractor suitable for the tonearm, this shouldn't affect the sound.

I'll defer to Doug's view on the effect, but I still think you can straighten it by rotating the arm in its pivot. If you look at this picture, you can see one set screw that fits horizontally into the pivot plate (ie the round plate that fastens to the plinth). If you loosen it with a hex key you the arm will become free so you can adjust the vertical alignment as well as the alignment to the plinth. Finally - forgive me for stating the obvious - be very careful of your stylus is you loosen this set screw. You may want to prop up the arm with something so the vertical position can't drop.

This is how Linn arms adjust VTA. If it were me, I'd straigten it, though I would not redrill the mounting holes.

The only relevant parameter in locating the tonearm on the plinth, is the distance from spindle-center to tonearm-center. At the correct distance, the tonearm can be located anywhere around spindle. If the tonearm is not parallel with the edge of the plinth when at rest(and this bothers you) then move the tonearm rest so that the arc of the tonearm when it's at rest stops so that the arm is parallel.

I agree with Bdgregory. If you can rotate the arm without changing the distance from pivot-center to spindle-center, that would work. But it is only an aesthetic issue! The outer edge of the plinth could be cut at any angle and this would not affect the turntable's function (e.g., the edges of the "box" could be cut to make a triangle, or a cirlce if that were aethetically sought).