Ooh, FINALLY a topic I can contribute to with some authority, for a change!
I own many ukuleles. I have played hundreds more.
In my experience, there is a huge jump in quality between a $25 uke and a $50 uke. 50 to 250 are mostly about the same, then there's another notable step up at about $400.
Anything above $500 and you're paying for provenance, or marketing gimmicks. There are hundreds of working luthiers charging over $500 for ukes, claiming artisan hand crafted wizardry and art, but in truth every uke on the planet is hand made. There are no ukulele-making robots.
The jump from 25 to 50 dollars is the difference between plastic and real wood, though there are some fantastic plastic ukes out there with just wooden soundboards. Beyond $50 you're upgrading from spruce and mahogany to koa and rosewood, but acoustically it makes no discernable difference because shape and thickness and bracing are more important to tone than the type of wood you use.
Bad ukes have poorly set bridges and tuners that slip, and they will buzz even with good technique or the intonation will bend as you move up the fretboard because the spacing is wrong. These are problems even a $25 uke should not have.
My kids play $25 ukes. My cheapest is a $50 maho/rose electric soprano, and I love my full koa tenor with the abalone insets as it is a thing of beauty. But I play my plastic Magic Fluke the most frequently, because it is awesomely loud and durable enough to live in my living room with three kids and two dogs. And because it stands up by itself.