Just some more thoughts on this.
I'm convinced this is definitely an issue affecting Safari, though as I say I think Flash might be a factor.
It seems to me that the problem is going to be very difficult to pin down, because (talking generally) you need to be especially observant when watching out for the symptoms. First of all, it seems to affect only the Amazon site. And I've found, for instance, that the beachball doesn't appear straightaway; it sometimes takes 5 or 10 minutes of browsing at Amazon before the hand pointer, when pointing at links on the page, suddenly changes to the standard arrow and the page then freezes and the spinning beachball appears. You then have no option but to quit Safari. It's going to be a slim chance that other Safari users visiting the Amazon site will see this, especially if they normally rush at things; the beachball most certainly doesn't immediately show the moment you go to a page.
This means that any technical people at Amazon, or Apple themselves, will not be able to immediately confirm the issue (and they therefore might not trust what you're saying). So therefore anyone who contacts Amazon or Apple will need to emphasise that several minutes will need to be spent on the Amazon site, clicking here and there, before the beachball's likely to appear.
At present I'm still questioning whether the Amazon site requires Flash to work fully. I've tried running some experiments to find out (using the Security settings in Safari > Preferences > Security) but in the end couldn't conclude one way or the other; the beachball seemed to appear, in the end, regardless of whether I allowed the site to use Flash.
Incidentally, my Flash is not fully up to date, but given that blountcomick's is, I'm not viewing that as something of any real importance. BTW, one question that's come to mind is: If you set up Security to block Flash from running on a site and then you later decide to allow it, will it work, or will it remain blocked? And vice versa? Does removing the site completely from the Security listing put the block/allow position back to a null state?
One other thing to observe are the entries in the Privacy box in Safari's Preferences, as they seem to be 'all over the place'. Trackers like 247-inc, betrad, etc get included there and though you can temporarily remove them they come back. I strongly recommend that you take a look at your cookie listing and monitor how its contents change if you do any more experimenting with this problem. I've a feeling that the cookie listing is somehow corrupted and is related in some way to the beachball effect.