Yes, the nut slot may be a little too high. Check that by pressing the string down lightly at the 2nd fret and looking at the clearance between the string and the 1st fret. There should be just a tiny bit of clearance, just barely the thickness of a piece of paper.
The other thing is that you are probably pressing too hard. When you squeeze the string hard right behind the fret, you make it go sharp. Lighten up your touch. No need to mash the string down against the fingerboard. Just press it enough to contact the fret. Try it with your tuner hooked up. Watch how you can make the note go sharp by how hard you push down on the string.
Last edited by Bruce Johnson : 07-13-2013 at 01:21 PM.