Don't worry about measuring clearances over a fret - let your ears or tuner tell you when nut slots are low enough.
You should be able to fret each string at the first fret without the note pulling measurably sharp. Note that "normally" means just behind the fret (not next to the nut) and just hard enough to get a clear note. With the tall frets they tend to put on ukes these days you will be able to pull even a properly setup uke sharp if you put a death grip on the string.
I.e. if the E string is tuned spot on, then when you fret at the first fret you should get a spot-on F. Typical factory ukes (Kala, Lanikai, etc) often pull anywhere from 5 cents to 20 cents sharp. Work each slot down very slowly (a nut-slotting file is best, but a welding torch cleaner can be used if you're not planning on doing very many ukes over your lifetime). Avoid the small triangular "jewelers" files - the shape of the slot they make is very poor. String height will vary drastically with minor changes in string diameter and when the string is pulled down into the sharp "V" under tension it will tend to make the string want to stick and not tune smoothly.
Ramp the slot down slightly toward the tuners, this ensures that the string will "break" cleanly right at the fretboard-facing edge of the nut. If you file the slot straight or, heaven forbid, sloping down towards the frets, you will probably not get the best sustain and you may even have intonation issues (which is the very thing you're trying to correct). BTW, StewMac.com sells nut files - they're quite expensive but for most uke work you can get away with just one "double" file - the size where one side is .026 and the other is .032 has been all I've ever used on ukes in spite of the fact that I own a full set of the files.
You should work each slot down just far enough that the fretted note is not sharp. When you reach that point stop, and don't worry how high the string is above the first fret. I can honestly say I've never measured the height of the string over the first fret. Ever. If you go too far (the string starts buzzin) you can use a bit of Nailaid Maximum Iron Hardener (nail hardener) to build the slot back up. If you've been working down slowly just one thin coat will probably do. The hardener will feel dry in a few minutes but let it cure for at least several hours (preferably overnight) before putting a string back in the slot. It takes several hours for the hardener to fully cure.
If you have one or more strings that you can't work down far enough to get perfect intonation at the first fret without buzzing then you have other issues. The bridge saddle may be too low, or the frets may not be even. If the action is very low over the 12th fret you can probably replace or shim the bridge saddle. If the action over the 12th fret is not very low then you have a decision to make. You can either level the frets or use the nail hardener mentioned above to raise the slot high enough to make the buzz go away.
Many folks are happy if they get the intonation at the first fret within about five cents without buzzing. I used to be (there was a time when I was happy with 10 cents, actually). However, the more you play, and the better intonated the instruments are that you play, the better your ear will become and the less tolerance you'll have for intonation issues. I can't really deal with five cents any more. There are certain first position chords that will drive me nuts if a string is off by more than a couple of cents.
Since most players spend a lot of time at the first postion I consider intonation at the first couple of frets to be the most critical aspect of a proper setup. Well, second only to the uke should not buzz when played normally, obviously. When you get the action low enough to get perfect intonation at the first fret, you'll coincidentally have a nice low action that will make that Bb, for example, much easier to finger.
My second step in a setup is to lower the bridge saddle until I am comfortable with the action up the neck - or until a string starts buzzing.
So, to summarize in order:
1) Work the nut slots for perfect intonation at fret 1
2) Work the saddle until happy with the action up the neck (12th fret and beyond)
If you encounter buzzing:
3) If the action up the neck is quite low, raise the saddle.
4) If the intonation is perfect at the first fret, see if you can raise the nut slot without introducing an unacceptable amount of intonation problem at the first fret.
5) If 3 and 4 aren't acceptable (i.e. the action is already fairly high or the intonation at first fret is already less than perfect) - you need to level the frets, and that's a whole 'nuther post.
John