Replying to this thread, plus having just restrung my uke and been talking about that, inspired me to work on the action and intonation of my uke!
I abhor wound strings, so what I have is Low G with solid strings. Basically, the thinnest fluorocarbon strings I could find.
Every uke is different, but I was able to get the intonation nearly perfect with just standard action adjustment and a little bit of work on intonating the saddle. I'd resisted doing this for over 2 years because a) It's the nicest uke I've bought, and I didn't want to mess it up (yeah, I know saddles and nuts are easily replaced), and b) it was SUPPOSED to have been professionally set up by Mim when I bought it. I've been putting up with crappy intonation on the G string since I bought it!
So, I first pulled the saddle (pro tip: Put something under the strings and slide it towards the bridge and you can probably slide the saddle out without having to remove or even loosen the strings) and lowered the action at the 12th fret to around 2.5mm.
From there, I found that the 12th fret intonation was sharp on C, a little more sharp on G, VERY flat (23c) on E and a little less flat on A. I played with placing a toothpick in front of the saddle to verify that I was moving things in the right direction. Shorter string for the flat ones. And it almost didn't seem like I was going to be able to get far enough with a standard saddle! (but, my toothpick was raising the action, which threw off my perspective)
Pulled the saddle again, and filed the angle of the top such that G and C were contacting further from the nut (longer string to make those less sharp), and the E and A strings closer to the nut (shorter string to make those less flat). I went all the way with both adjustments. I can't do more without making some kind of a custom saddle. Worthy of note, this uke came with an round-top uncompensated saddle. I slipped it in upside down so that I could use the flat side as a basis for the intonation adjustment.
Fortunately, that was enough. Well, it depends on how you look at things. But, if I give the 12th fret JUST enough pressure to get the note, the intonation is nearly perfect. I never play up there, anyway, so it's close enough.
Next step: check the first few frets. Lowering the action at the saddle helped that a lot, too. It's closer than it's ever been. But, still off. So, I measured the action at the first fret, aiming for about .5mm. There was a bit more than that. I used a folded sheet of sandpaper to deepen the slots. I took the G string as low as I dared. The other strings didn't need as much, but I took them all down some.
Now, intonation on the first 3 frets is within 5c, again with a light touch. I'm pretty happy with it. I thought I was going to have to get creative with nut compensation, but it's not needed.
I'm going to tune everything about 2c flat so that when I strangle chords, they won't go too sharp. Should end up sounding a lot better than it ever has (and I've actually really enjoyed how this uke sounds over the past 2 years!), and the lower action is definitely easier to play.
Hope you have similar luck! If you're worried about adjusting your saddle or nut, just order a set of replacements to have on hand just in case you take something too far. Or, for the nut slots, you can always do the super-glue and baking soda trick.