#1
I got a new nut for my guitar, and now it's tuning is messed the hell up. I can strum a G chord and have it perfectly in tune, and then I strum an E and the e and B strings are flat a quarter of a step or so. If the G string is tuned about a quarter step high, everything (not including first position chords) sounds great. Barre chords, and any classical song in the middle of the neck. But my first position chords...

Any idea what's up?
Winner of the 2011 Virginia Guitar Festival

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#2
Are the slots the correct size for the gauge of string you currently have on the guitar? The strings could be binding up in the nut slots if they aren't cut to the proper size, which will in turn give you tuning/playability issues. You could try some lube at the string to nut contact point. This is good practice irregardless if you have tuning problems or not.
Also, be sure to check on the break angle of the nut. That's the angle across the top of it, where the strings ride. Too severe(slanted down toward the headstock side of the nut) and your strings will tend to bind on the neck side of the nut. This is more likely to happen to the wound strings than the plain. The wraps are perpendicular to the length of the string, but the string needs to be able to move freely lengthwise in the nut slot, so the wraps interfere if the angles aren't right on.
The B and high E strings should be able to slide decently enough in the nut slots, so it might be that the nut's leading edge position was changed(edge closest to the neck) when you replaced the nut. This will have the same effect as adjusting the bridge saddles on an electric, shortening or lengthening the scale to acheive proper intonation. Since you said the B and E are flat relative to open, then you might need to bring that edge of the nut closer to the neck.
Buzz Feinten has a deal called a "shelf nut", which compensates intonation issues up at the headstock end of the neck. Google it to read up on what's involved. Might give you some other tips on what to do.
Hope this helped out.
#3
Yeah, I actually went out to my teacher. The nut was the right size, but it wasn't glued in strong enough so it had broken off and was sliding and rotating slightly depending on how hard I strummed or if I changed the tuning drastically.

But thank you for the reply!
Winner of the 2011 Virginia Guitar Festival

Protools HD
Lynx Aurora 16/HD192
Mojave, Sennheiser, AKG, EV etc mics
Focusrite ISA828 pres
Waves Mercury
Random Rack Gear

65 Deluxe Reverb
PRS CE 22
American Standard Strat
Taylor 712