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No. There is no keyboard shortcut to do spell check. It is probably more useful to use the mouse because sometimes there could be multiple suggestions of what word you meant to type.

If you are in the middle of typing a word, you can usually press the escape key and a menu of suggested words will pop up.
 
You can move between misspelled words using ⌘-; and you can open the spelling dialog box with shift-⌘-;
 
Is that in a specific application or in any Apple application?

It should work in any applciation that uses the Mac OS X Spelling service: Safari, Mail, TextEdit, Pages, Keynote. Pull down Edit > Spelling > Spelling and see for yourself.

It won't work in Microsoft apps, where the Spelling shortcut is option-⌘-L, because Microsoft has to be differrent.
 
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