The strips in a feeler gauge are made of steel or stainless steel. Most of us will be using just steel and will need to keep them from getting wet. They can rust and throw off the thickness of the gauge. But the more important issue is that we are using just the edge of the strip. The strips are very exact. If you put your digital calipers on a strip and it is off by .0002, it is just as likely that it is your caliper that is off.
But there is somewhere on the strip that is likely to be inaccurate. Unfortunately, it is right where we need it to be accurate. The little strips are "punched" out of a larger sheet that is accurate as to thickness. The punching process tends to deform the very edge of the strip. Think of the process like a cookie cutter. Let's say that we have a sheet of cookie dough that is exactly 1/4 inch thick. As the cookie cutter passes through the cookie dough and cuts out the shape, it deforms the edge of the dough by rounding it off. The perfect thickness is retained on the entire surface, except at the edge where it is no longer 1/4 inch thick. And that edge is exactly what we are using when we measure with our feeler gauges.
The amount of deformation on the feeler gauge edges varies with the brand of gauges and the thickness of the gauge. I haven't found any that are perfect right out of the box. Fortunately, it is something that is easy to fix. And it is one of those things that is so easy to fix that there isn't much point in trying to determine which or how much a feeler gauge edge is deformed. It will drive you crazy trying to look at the edges under high magnification, which would be required (at least for my eyes). Some of these pictures are through my bench magnifying glass, and even still it is easier to describe than it is to see.
In the above picture, I ran a black Sharpie down the edge of a .016 inch feeler strip. I was then going to run then run the edge over sandpaper to show that there was a little strip of Sharpie not removed. That would indicate the "rounded off" edge of the feeler gauge that we are going to fix. Unfortunately, getting a good photograph was impossible and I was spending way more time trying to get a picture than it would take me to just finish the edge to 90 degrees and make it accurate for mouthpiece refacing. Think of this process as "sharpening' your feeler gauges, although the sharp edge that we are looking for is 90 degrees.
This is basically all you have to do (to both sides on the various gauge thicknesses). I'm using 320 grit, which is aggressive enough to cut through the steel without leaving any burrs. I'm only sliding the gauge along its length, not crosswise. That ensures that there will be no burrs. This paper is on top of a piece of glass, just like I was putting a facing on a mouthpiece.
The above picture is what I'm going for. After "sharpening," I have a sharp, crisp transition from shadow to shine. It isn't really necessary to get carried away with magnification. You can feel the difference on the gauges, especially on the thicker ones.
Run your thumb over the edges. Before you start the sharpening process you will notice that on one side of the feeler gauge both edges don't feel as sharp as the other side. (The rounded edge has always been on the etched side on the ones that I have.) That is because of the punching. You want both edges to feel sharp. On a gauge like the .010 inch, that takes about 10 swipes back and forth on 320 grit. If you have some of the larger thicknesses, like .050, it will take longer. Also, if you have the longer gauges (I have some 1 foot long ones), it can take considerable time.
If you can remove the individual feeler strips from a bundled set, that makes it easier, but this can be done on the mechanic's sets that are permanently bound. Be careful on the really thin ones, as you can put a kink in the steel. Also use something like 600 grit and a light touch. And you don't have to do the entire set, of course. Do the ones that you use individually and in a stack. Even in the stacked blades, you don't have to do the one(s) that are always in the middle. For instance, your .021 blade is only used as the center blade when stacking .020, .021, and .023 in order to measure .063.
If you are concerned that you might have put a burr on the edge, run your fingernail down it. Or pinch a piece of bronze wool over the edge and draw the strip through. Be careful not to go over the chemical etching on the blade, as it is easily removed.
So how much does this increase the accuracy? By less than a whole Brand number (.5 mm) at the most on any that I have sharpened. But it makes enough difference that you will notice. I have measured, set that feeler down and measured with another strip, gone back to the first one and, wait a minute, it measures different now!! That's because I inadvertently flipped the strip over. When the rounded edge is on top it measures different than when the flat edge is on top. Sharpening the edges on the feeler strips gets rid of that.