Broke out my old copy of Jumpin' Jim's 60's Uke-in and went over some songs that I tried when I was brand new. I may be easily amazed, but I am always amazed at how songs that once seemed really difficult are suddenly easy after the passage of time.
One song that I tried early one was Dock of the Bay. That's a song of my generation that I have always liked, but it had the dreaded E Major, a chord that, in it's first form, is train-wreck for my fingers.
Since learning the magic of the barred chord, I found Dock of the Bay much easier today. If you bar the chords, the whole song becomes much easier. I'm all about what's easy.
One thing that still throws me is when I try a song where the rhythm of the strumming and the rhythm of the melody are at odds. Like in reggae. If can strum a vanilla rhythm and it sounds ok to me. But I have trouble when I try to do anything else. Under the Boardwalk is a good example. The chords are pretty easy. But the rhythm screws me up.
There are a few songs that, if I just figure it out instinctively, I'm OK. It's when it's on paper and I try to learn it that way that I have trouble.
Anyway, the whole point of the ukulele first is to amuse myself. If I ever actually get good, that's just a plus.