My single biggest complaint is the 30 day return period. If you want to return something because you just don't like it, you will probably pay for the return.
It can be hard to get to the return policy for a supplier; if not stated at all, it is an Amazon return policy. I have found, though, if I gripe about paying for a return, they usually capitulate. They have no physical store like many other online suppliers do, so it is harder to return an item. Items come defective/broken too often.
If you are a Prime member, reviewing the monthly statement is a hassle because you have to open the Amazon Orders page as well as the bank page and compare each other. What's good: Amazon sells practically anything.