I use an Intelli Touch IMT-500 tuner;  after I pick the G string, the screen often shows G at first then D and then goes back to G. This happens even if I mute all other strings, including the paired G. It is a brand new Mandolin, that came set-up. Any suggestions as to what may be going on?

Not a big deal. A lot of times these type of tuners (especially if low batteries) that pick up vibrations will display the 5th of the intended note. Like sometimes the E strings flash as "B" etc. I'm sure there is a Physics explanation concerning harmonic frequencies and such, but I wouldn't bother.

Just know that when yours shows up flashing between a G and a D, it's in tune. Better yet, hit a harmonic at the twelfth fret and you tuner should show G.

Yah that happens. I find that if I clean the part that clips to the headstock and maybe even the headstock sometimes I get a better reading

A couple of things might help.  First, try tuning using the 12th string harmonic instead of the open string.  You sometimes get a better reading.  You might try moving the tuner to a different part of the headstock.  I found out something the other day that was really interesting.  I read that Bryan Sutton clips his tuner to his strap near where it connects to the neck heel.  I tried it and it works nicely.

I tune by ear and like to teach my students (when they are ready) to tune this way.

That's 'cause your an old guy. There was a time when we all used to do that,that or be out of tune. I think everyone should know how. I used to crew on sail boats in the South Pacific ,it was handy to know how to navigate even though there were all these new electronic calculators and such to do it for you. This was before you could track yourself by satellite but the principal is the same. Every so often some couple that had been sailing from Marina Del Rey to Catalina for years would decide that they would head off for Hawaii, they didn't know navigation but they had all the electronic aids. One thing though, when you get out away from shore and you've been in the salt air and everything is wet always the first thing that goes is your electronics. So 190 days later heading out to Waikiki they make landfall ,half dead, somewhere on the Tuamotos or the Philippines, kiss the ground and never get on a boat again.. The electronic tuners are really nice, you can tune in a noisy room or figure out your not in tune which can be difficult to tell in the same noisy room. But if you don't have one sometime or your battery goes dead what are you going to do? I rely on my electronic tuners but I still carry my tuning fork with me.

Agreed on knowing HOW to tune by ear, however, I've found that if you are playing with several other players, not everyone hears the same or not everyone has that perfect ear for pitch. I played with a couple of guitar players that refused to use tuners because they thought they were too good for that. Believe me, they were not. They were horribly out of tune and you could REALLY hear it on live recordings. It used to really get on my nerves. My take is it is a good skill to have, and use it when you find yourself without a tuner. But if I have one, you can bet I'll be using it, especially if the other players in the Circle are...