I normally use my gedit spell check extension for the task, but wouldn't it be much better if you could fix any typos or otherwise during compilation time, in a sort of interactive mode?
You can let TeX (rather luaTeX) do the spell checking for you! For example, in ConTeXt MkIV, you can use
en is the current language (you can set different word lists for different languages), and
wordlist.txt is a sorted list of correct words. For a complete example, see the ConTeXt wiki
It seems unreasonable to implement spell checking as a LaTeX package when there are excellent spell checkers for the terminal that can be incorporated into the compilation process. Before you compile you can do
aspell -t -c file.tex
ispell -t file.tex
Either lets you interactively spell check the whole file. The
-t option is to tell the spell checker that the file is in TeX or LaTeX format so that it will ignore macros.
To combine this with the compilation process you can invoke them after each other such as
aspell -t -c file.tex && pdflatex file.tex
or you could make an alias to shorten the command you need to write. If you use
latexmk you could make it run
ispell for each compilation by a using a technique similar to what is described in https://tex.stackexchange.com/a/42166/5701.
If you prefer to simply get a list of misspelled words non-interactively, you can run:
cat file.tex | aspell list -t | sort | uniq
Not an interactive solution, but you might want to have a look at the
spelling package. The package requires the LuaTeX engine. Only the LaTeX format is supported, but support for other formats shouldn't be too hard to implement. Contributions are welcome!
If you use sublime text as an editor, you could try https://github.com/vaisaghvt/CheckTypos package.
Not professional but still as an option: if one has Microsoft Word on the system, one could copy and paste the LaTeX source into Word, and following the red lines to correct them.
TexStudio does spellchecking and underlines misspelled words. It also has a spell checking menu option. No need to compile.