High strings at the nut can cause sharp intonation and make playing in first position difficult, while low or worn slots can result in open-string fret buzz. Generally, the bottoms of the nut slots should be a few thousandths of an inch higher than the tops of the frets when the neck is straight. To check nut-slot height, hold the string down at the third fret, and see how much it moves over the first fret. This is similar to checking neck relief, but the string should move much less. If the string doesn’t move at all, chances are the slot is too low. If it moves more than a few thousandths of an inch, it should be filed lower.
If you find that a nut slot is too low and your neck has the correct relief, filling (not filing) it can work nicely. I use bone dust, but I’m guessing most of you don’t keep that in your spice rack. Baking soda works great, too, and is easy to find. Pack the slot bottom with baking soda, clean away the excess, and then apply thin superglue. Use a toothpick to apply the superglue until the baking soda looks wet, being careful not to get any on the peghead. For best results, let the fill cure overnight. The glue will harden to the point that you can file it like it’s part of the nut.
You’ll need a set of nut files to properly lower the slots, but a triangular needle file may suffice as long as the slots aren’t too deep in the nut. Try to keep the slots spaced evenly and angled down so the highest point is where it meets the fingerboard. If you accidentally file the slot too deep, which still happens to me once in a while, grab the baking soda and fill ’er up. You may find it useful to use a feeler gauge a few thousandths of an inch thicker than your fret height in front of the nut as a reference when filing.