Any measuring tool or device for checking level can be mis-read. So can rulers.
Right, and if it requires extreme care to avoid mis-reading it, then the chances are much higher that you will get a wrong reading than something that is easier or has more inherent accuracy.
Lauri is right, the usual standard for instrument accuracy is 10X the required measurement accuracy and some things probably, ideally, are measured to 1/10th of a degree - not many, but at least some. I am at least a little skeptical about reading small bubble levels (say, a 1") repeatably to .01 degrees. For most things that is plenty good enough, but maybe not for a few critical measurements like the stab incidence.
Mostly we get by with far lesser methods by being able to trim and adjust-in-test, and at some point you can't count on alignment stability being good enough over time or conditions, so I am not really criticising the idea. Most people don't bother measuring anything at all, just cutting out the fuse sides and hoping they did it (or the die or laser) cut it well enough. But to make good sense of your results, a few things you really do need to measure to decent accuracy.
in the spirit of full disclosure, I do not have any precision levels or incidence meters at all. I use trammelling from a reference surface that I think is good to about .005, and the biggest issue is not the measurement itself, but determining the reference points on the airplane itself (like, where on the LE of the wing is actually the aerodynamic "0" point). Note that the reference surface is a piece of melamine board over a very carefully planed and sanded butcher-block birch that I have tweaked over the years using precision straightedges, updated before every atab alignment. I check the melamine surface and shim it straight WRT the base using indicator dust (chalk). Even then, I would guess I can measure repeatedly to about .005", which is about 3x better than the stab incidence angle I am trying to hit. If I had Lauri's gadget, I would use that.
Note also that the "flat stab" is not flat because that is aerodynamically better, it's because it can be accurately measured by naturally providing a very good reference. You then make it pointy to get it to work better aerodynamically. I use an airfoiled stab that limits the measurement accuracy but (I think) performs better.
Brett