Spell checking in emacs
One of my favorite minor-modes in emacs is the flyspell-mode. It
continuously marks all words not found in the ispell-dictionary as you
type. It’s particularly useful with AucTeX because it skips comments
and TeX markup.

If you want to invoke flyspell-mode everytime you go into
LaTex-mode, add this hook to your .emacs file:
(add-hook 'LaTeX-mode-hook 'flyspell-mode)