I hate that I need to log in 3 times within the space of 5 minutes as I hit different parts of the site that apparently are considered more and more sensitive.
I hate the way they keep on misleadingly suggesting that items might be eligible for free shipping when they aren't (every possible signal from the user profile to ip geo-location should be indicating that I'm the wrong country for that).
I despise the way they keep on defaulting me back to paying in the wrong currency with their rip-off "amazon currency converter" with worse exchange rates than my credit card.
I can't believe that in this day and age they aren't able to synchronize anything except the most rudimentary profile data across their different domains. So the US site will keep on recommending a DVD I've already bought off the UK site, and the UK one will nag me about rating a book that I've already rated on the US one.
That's just a few things off the top off my head, not some long held grudge list.
I think I was caught in a little bit of Silicon Valley myopic thinking since their site isn't shiny and that's what is mistakenly considered as interchangeable with good UI design these days. That being said, Amazon.com the site does still need to improve UX in a couple key areas. Compared to more contemporary e-commerce sites, the ability to compare items and make sense of ratings (i.e. the flaws of the 5 star rating system) is where they need to make the most improvement IMHO.
It may have been an overstatement to say "their site leaves much to be desired" in all fairness.