this is a funny thread because the ukulele playing in tune has more to do imo (maybe I am wrong) with the strings than the ukulele. I so far have had a kohala (cheap lanakai) and a pair of dolphins and a makala tenor and a cordoba. The cordoba came with aquilas. The other instruments all came with those brown nylon strings. The Cordoba is the only of the instruments that REALLY stays in tune all the time. It is also, by looking at it, the one with the most attention to detail and looks the nicest of the bunch.
We're talking about playing in tune - up and down the neck - not staying in tune - as in holding a tune. It's called intonation and it's affected by several things. One, of course, is the frets being in the right position but that isn't an issue on modern instruments (though if you want to get really technical you could discuss even vs. "just" tuning for a decade or two).
On most factory-built inexpensive instruments, the slot in the nut is too high. This results in very poor intonation at the first couple of frets. I.e. if the string is in tune at "C" for example, when you finger at the first fret you don't get a C#, you get something higher than a C#. When you press down on the string behind the first fret, it is at a very steep angle from the nut and pulls the string sharp, often by as much as twenty cents or more on inexpensive ukes. Filing the slolts in the nut lower alleviates this problem and restores the intonation at the first fret. However, if your frets are not perfectly level or the neck relief is not right, you can't take the slots low enough to eliminate the strings pulling sharp without introducing a buzz.
Intonation at the twelfth fret is primarily a factor of string tension (unless the bridge is extremely high). Theoretically, if all of the strings were under exactly the same tension the intonation would be identical across all the strings at the twelfth fret. In practice the tension is never exactly equal across all the strings, and in most string sets the manufacturer intentionally chooses gages that will make the lighter strings under more tension for balanced volume. Often on guitars you will see angled bridges to help with intonation - and also often compensated saddles. Because the uke has two small, high tension strings on the outside and two lower tension strings on the inside you can't really achieve much by angling the bridge. Therefore, most ukes will either be a little flat or a little sharp on two of the strings, at the twelfth fret (actually all the way up, but we usually measure at the twelfth fret). The bottom line is that unless the bridge is
very high there isn't a lot you can do about twelfth fret intonation except try different strings.
Fortunately, I've found that intonation at the twelfth fret isn't off by more than ten cents absolute, and about five cents string to string, on most of my ukes. That's in the same general ball park with good guitars.
So, for most inexpensive ukes the biggest issue is getting that nut filed down - though if you can't get it low enough you also have to level the frets. It's tedious work and that's why I'm perfectly happy to let somebody like MGM or Mim or whoever do it for me!
Oh, and another thing affecting intonation is fret height and fingering technique. I've got guitars with jumbo frets that I can pull twenty cents sharp just by pinching the string hard right behind those big 'ole frets.
John