When I active flyspell, M-x flyspell-mode, it marks misspelled words as I write them but it does not mark any misspelled words in the buffer that I have not written during current session. How can I make it so that flyspell also marks misspelled word not written during the current session?
Well, you can manually do:
M-x flyspell-buffer
If you want this to happen every time you turn on flyspell-mode, you can add this to your .emacs:
(add-hook 'flyspell-mode-hook 'flyspell-buffer)