The built-in ASC spell checker is -- to put it kindly -- quirky. First, you must turn it on using the 'abc' tool on the right in the editor toolbar. (When it's on, it highlights.) But it won't stay turned on if you click on the tool before you enter any text -- it will just tell you that no misspellings were found & won't stay on. It also sometimes fails to check the last word if followed by a space. You can tell it to ignore misspellings, but you can't tell it to learn words because the spell-checking dictionary is actually on the servers running the site, not on your Mac or PC.
But from your remarks, you probably aren't even using the built-in checker. Instead, I suspect you are trying to use the far superior system-wide one built into OS X. The problem with that is the ASC editing tools are powered by Javascript supplied by the Jive SBS software running the site. Because that is platform independent it doesn't know anything about OS X's contextual menu (which includes suggestions for misspellings, the Dictionary lookup, & so on).
So to make a long story short, what happens when you try to right click on a word the OS X checker has underlined in red, instead you get the Javascript's response to a right click, which brings up the editor's insert/alignment popup menu instead of the OS X contextual menu.
The solution is to control click on the word -- believe it or not, within the ASC editor window a right click & a control click are not the same thing! You literally have to hold down the control key on the keyboard when you click to bypass the Javascript's right click response.
To make things that much more confusing, this only applies if the pointer is not over empty space in the editor window, which in this case excludes lines that have any text on them, including invisible text like spaces or returns. (To see what I mean, drag the tab at the bottom right of the editor window down so there is a lot of empty space below what you have typed. In this empty area, right & control clicks both bring up the OS X contextual menu, but anywhere in the text you have typed, they behave differently.)
In short, the problem is not that Apple has changed how the buttons or clicks work, it is that the new software that runs the site (not developed by Apple) does.
Hope this helps.