Their dispute resolution service is annoying a hell. Not that we don't want to resolve disputes with our customers, but we want to do it using our existing customer support channels. Not via PayPal. Having customers just randomly getting their money back without having contacted the business they bought the product from first isn't acceptable.
It's the most expensive of all the payment solutions we offer our customer. Developer support is okay, but not helpful when their stuff doesn't work. We randomly get 500 errors from their REST api, which doesn't handle any sort of real volume. Black Friday pretty much killed PayPal.
The PayPal web interface is the worst I've ever used. It's slow and almost impossible to search in. Searching using your own order numbers almost never works and you fall back to searching for customers last name, which is pretty much the only search that consistently work.
We wouldn't use PayPal if our German customers didn't expect it.