It works fine with Amazon here. I can't speak for the other sites you mention, but it works for the majority of sites out there. The ones it doesn't work with are generally poorly-designed.
If you're finding it doesn't work for sites that are working fine for other people, you may have a Safari extension or internet plug-in or some other software that is screwing things up.
I wanted to make it clear that I am not talking about the publically accessible Amazon Store but the Amazon Web Store which is used for those who have an online shop or set up e-commerce.
The fact that Amazon is a large company does not protect it from making a crappy site. If its e-commerce pages don't work in Safari, that's laziness on the part of their web developers, pure and simple. There's no reason for a modern web site to fail to work in any standards-compliant web browser. This is something you'll need to address with Amazon.
I have exactly the same problem - of coutrse works fine to buy things on Amazon but not to set up your own store.
I messed about for a few hours and have now switched to firefox which works perfectly. Surprised a company such as Amazon have not addressed this. (by the way some of the websotore features do not work with chrome either).