What method do you use to check if the bottom bracket needs to be face? Is using a caliper to measure the length at various points on the bottom bracket a good enough method?

Someone around here has suggested using a feeler gauge to determine if there are uneven distances between an external BB cup and the shell.

If the BB shell's rim has concentric tool marks made by the circular motion of a facing tool, then it's been faced and you don't need to do it again.

When I see a BB that I'm not sure needs facing, I paint it with a magic marker, or toolmakers dye, then do a light pass with a facing tool. If it removes the dye over 270 degrees, it's fine and I don't have to face. Otherwise I face until I've achieved at least 300 degrees of face, which is needed for supporting cups flat. (low spots don't count, the cup is oriented by the high points of contact, so theoretically 3 areas forming a triangle would be sufficient)

For a home mechanic, you can test by putting a thin grease film on the face or cup, and watching to see if it squeezes out evenly most of the way around. But if in doubt, a skim pass with a facer is to only definitive way to know.

Tighten the cups until they contact a .010 inch feeler gage, then use .008-.012 inch feelers to check for high or low spots. All paint should be removed from the faces of the BB shell before doing this.

I don't agree with the 300 degrees, unless it's a typo. It's an unbroken 360 degree ring that is the proper test of complete facing. The ring does not need to be the full width of the face. 300 degrees leaves 60 degrees left of a possible

Caliper tells you nothing. With a painted BB shell it's evident either by tool marks or removal of point that facing may have been done. If there's any doubt, measure the width and face it. Severe BB shell facing errors show up in bottom brackets after installation as binding all around/unusual spots. Or a BB that spins fine until it's fully torqued.

Paint the faces with machinist's blue and run the facer over it lightly. If the bluing is removed unevenly, it needs facing.