There are about 3 (well, more but 3 to start) basic nut issues.
The first one is not having the slots cut an an angle so they are a little deeper on the headstock side than the fretboard side. If they are not angled you will get a sitar sound.
Another issue is the fret slots are too narrow for the strings. When you try to tune you are basically trying to force fit the string into a groove that is too small.
The last one is height, but if it is too high it doesn't sound bad, just out of tune. If too low it will buzz.
If you haven't glued in the nut you can work it, and as stated above it is time consuming, but not that difficult. You will need to get really narrow files, or welding torch tip cleaners (Harbor Freight). I actually found some mini dremel rasps that I first used (by hand without the dremel) until I bought real nut files.
John