I've been playing mandolin for years, and I tune it with no particular problem (insert mandolin tuning joke here). But, while in theory I believe it is impossible to tune a mandolin or other stringed instrument perfectly while maintaining intonation, I think there are some tricks and techniques that help.
Assuming that the instrument has been properly set up (string height, scale length, etc), what can one do to get the best tuning for a particular session? I know that the instrument goes out of tune due to changes in temperature and humidity - usually sharp for mandolins.
One person [rvk] says to "catch and release," which means to slacken the string below the desired tuning, then always bring the tuning up to the desired note. Presumably this accommodates the string's sticking at the nut and bridge.
Online videos about guitar tuning suggest tuning slightly under the desired pitch by a few cents to balance the added tension of fretting, especially heavier strings. So the G string(s) might best be tuned to, say, -4 cents.
I have discovered that stretching a string that is slightly sharp, by pulling it sideways with the plectrum, is a convenient way to lower the pitch a small amount without using the tuning peg.
When putting new strings on, I usually have to do multiple tunings because tightening one string has the effect of loosening all the others a bit (why I think that in theory tuning is impossible :) I also stretch the strings by pulling them sideways as noted above, but more aggressively than for minor adjustments. Incidentally, I use a tuning tool to rotate the pegs for new strings - so much easier than doing it by hand!
Ok, that's what I think. Any suggestions, tips, tricks?