Thanks very much for this link. That feedback link is exactly what I was looking for when I first came here and started this discussion. I was hoping to be able to give that feedback directly to Apple, but they do not make that feedback site easy to find. All I could find was this forum, so I posted hoping Apple would see my comment and that others would also chime in to report the same issue.
I have now sent feedback to Apple on this issue, and I hope others are doing the same.
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In case anyone's wondering, getting a brand spanking new iPad Air does NOT solve these problems. I got my iPad Air last week, and I am still having these issues with Safari and iOS7. They seem SOMEWHAT mitigated (e.g., I have been able to play the occasional embedded video on some sites that crashed in the past, but then the same pages will crash at other times.) But these problems are still cropping up several times a day, which is several times to many. (And they persist even after installing the most recent iOS update. If anything, they may be a little worse on the iPad Air after that update than before.)
To recap, the main issues are:
Safari tends to crash on a regular basis, with no apparent pattern regarding particular sites or content thereon.
Crashes are especially common, though not limited to, sites that include embedded video, especially if you try to play said videos or just accidentally click on them.
Switching between Safari and certain other apps will cause Safari to "reset" itself, causing you to be logged out of any sites you happen to be logged into.
Switching between the above mentioned apps and Safari will generally also cause those apps to "reset" themselves, meaning lag time when multitasking back to them and losing your place in the other app, needing to start over.
Using a different browser does not necessarily avoid these problems.
It is very frustrating that these problems persist even after upgrading to Apple's latest and greatest hardware. I was always planning to get the newest iPad, and my excitement about it was already tempered by the idea that the new iOS seemed to make the upgrade necessary rather than just desirable. But to shell out the money for the iPad Air and STILL have these problems is getting ridiculous. APPLE, PLEASE FIX THIS!