My Tuner (a Korg CA 30) can't seem to make it's mind up if my top string is in E or A. It starts on E but then flickers between E and A.

Is this is a usual issue. Or am I looking at a faulty unit. I am beginner and it is the first tuner I have had so wouldn't be able to compare it with anything else.

My chords sound ok so pretty sure the string is in fact tuned to E

fret the 5th fret E string and open A string, if they sound the same, win.
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Yes, that is a common problem that occurs with tuners from time to time.
probably just your a string ringing from when you pick the e string, it happens from time to time, just mute the a string when you tune.
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tuning to a harmonic (12th or 7th fret) will give a more pure frequency with less overtones.
also try rolling your tone right back and using a mid range volume rather than full, should reduce the amplitude of the overtones going into the tuner and so confuse it less
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Mine does the same thing. It always says the high e is the low e but It tunes it correctly. It's just says it's messed up. Try using both the neck and bridge pickups.