Yea, like when I'm typing and a word is misspelled, it has the red dashed underline where I can right click and choose a correct spellilng.
I'm fairly certain you can't do either of those things with the existing edit box. Probably the easiest thing to do would be to hook the function(s) that actually send messages you type into the frame; if there are no spelling errors in the message, pass it through, otherwise, pop up a custom frame showing the message with the misspelled words in red (underlining isn't very practical) and some facility for correcting them.
I'd end up smashing my keyboard in a fit of rage if WoW tried to autocomplete every word I was typing. Autocompletion is always the first thing I turn off in every program that tries to do it. Most annoying "feature" ever.
Also, if someone doesn't know the correct spelling of words (or is prone to hitting the wrong keys without noticing) it's not likely he's going to know which words he should tab complete, or want to tab complete every word. :p
I can see Phanx's solution being viable. God knows it can only improve the general chat channels. It would have to take into account wow slang off course (Mankrik's wife anyone?). Heck, it could 'learn' by reading quest descriptions and incorporating those words into it's dictionary :D!