After much sobbing of blood and gnashing of teeth, we have determined the actual issues folks are reporting following the TinyMCE upgrade!
Spellcheck doesn't work:
Although words are underlined with red squiggles in some browsers (others aren't getting squiggles), you cannot right click on the underlined word to see and/or accept the browser's suggestions. If you right click, you only get TinyMCE's context menu.
Additionally, the default Safari context menu includes a spellcheck option when right clicking on text. TinyMCE's context menu does not contain that option, ergo it is missing.
Paste option is missing/not working:
Baffling! Right clicking in the previous RTE never provided a paste option. But sure, let's add the useless Paste option to TinyMCE's context menu, since at least that will tell people to use the keyboard shortcuts.
Yeah, well. Turns out if you right clicked on a word, it provided the option to paste.
So! We're going to disable TinyMCE's godforsaken context menu (the next version enabled it by default) and all the normal browser behavior should be back.