SpellCheckAsYouType (SCAYT) product allows you to see and correct misspellings while typing. Misspelled words are underlined, and you just need to Right-Click a marked word and select a suggestion to replace it with.
Now SCAYT is available in a bundle with grammar check feature, GrammarAsYouType (GRAYT) for CKEditor. GrammarAsYouType allows to see and correct grammar problems while typing.
SCAYT is available as a plug-in for CKEditor and TinyMCE.