What I hate most are the ton of features which are supposed to be "discoverable." Or in other words, you have no idea they exist until someone else tells you about it (and how did they find out)?
For example, aside from the traditional way of adding a friend, you can point your camera, in Snapchat, at someone else's phone displaying the profile screen, and it will automatically add them as a friend. Only one other person I've met has known about it before I told them (and they're the ones that told me).
The UI also is just generally clumsy or buggy. Another example, just some of my gripes about the part of the app where you can text chat with people:
You get a push notification that "X is typing" whenever someone begins writing a message to you, even if they don't send a message. Every few days I get one of these notifications when a friend accidentally began typing to me instead of someone else.
They've replaced the "send" button on the keyboard with a button that livestreams your camera to that person. Quite a surprise the first time you're chatting and you're only in your underwear.
You have to hold one of your fingers on the screen the entire time you're video chatting. And you change between the front and back-facing camera based on where on the screen you are holding your finger.
I actually really like Snapchat, it's the only social network/app I use regularly, but damn does the app suck.