I've been experiencing the same issue for awhile now, and just this morning I noticed that if I'm in Safari (while holding the phone in Landscape mode w/ the proximity sensor covered or not), if I scroll up slightly so that the URL bar and the other tabs scroll into the margin at the top of the screen out of view, the screen will then respond to my clicks.
I can reproduce the issue 100% of the time if I open Safari while holding the phone in landscape, refreshing the current page, and then trying to tap any of the links on the page. It seems like something in iOS is failing to initialize the "content portion" (the viewable portion of the website you're visiting, below the URL bar) of the page for tapping (though scrolling works) until the user performs another action, i.e. rotating the phone into portrait and back to landscape again and then tapping, scrolling far up enough that the URL bar is not visible, etc...
I can't speak for the other apps (particularly the messages app -- that issue where a recording starts just because one is rotating is bizarre), but for Safari, I can reproduce the issue every single time doing that.
I know it's not much of a fix, but at least scrolling up a bit allows the page to be clickable again.
I hope this helps somewhat!
--Mitch