On a Mac, you can of course just open up a terminal, cd to the directory where you keep the TeX file, and issue
while true; do sleep 5; latex -halt-on-error filename.tex; done
and have the DVI file open in a viewer that watches for (and reloads on) changes. The one-liner runs latex continuously with 5 second break between runs (the -halt-on-error options prevents the incantation from getting stuck if you saved a file with errors). You can also swap in pdflatex instead.
This solves half of your problem. The other half has to be dealt with by your editor of choice. You need to set it up to automatically save the file every x seconds, and how to do that depends on the editor at hand.
Now, that one-liner I gave above is quite ugly and resource wasting, since it makes no sense to re-compile if no changes are made (Edit: See this comment below for a much better way to avoid this problem). So you can do something like
while true; do sleep 2; if [ filename.tex -nt filename.log ]; then latex -halt-on-error filename.tex; fi; done
which watches for changes to the TeX file (signaled by the fact that filename.tex is more recently modified than filename.log) and compile when necessary (with a possible two seconds delay).
Short of a WYSIWYG, I am not quite sure how you can achieve full real-time solution. Compiling the code takes usually a short amount of time (1 or 2 seconds, or more if the file is large). So if you are looking for a solution that calls the LaTeX compiler, it probably shouldn't try to do it more often than once every 5 or 10 seconds. So you won't be able to immediately see what you typed in the DVI window. Also, if the editor autosaves the file in a spot where you are halfway typing a command, then the source won't compile.
With LaTeX I feel that the better idea is "compile-on-saves", where the human initiates the saving of the file (as compared to "automatically saving and compiling in the background). For that, modern editors can generally support hot-keys where saving and compiling is mapped to one keystroke. In vim I map F2 to compile and F4 to call XDVI.
Try compiling with
pdflatex -file-line-error <filename>
That way, the .log file will generate C-style errors which begin with filename.tex:12:Error message, for an error on line 12; I think vim may even have built-in mechanisms for parsing these, or if not, making a regex for finding them in the log should not be hard.
As others have mentioned there are Vim plugins that have built in methods for dealing with LaTeX errors. Personally, the Vim-LaTeX (AKA the LaTeX suite) plugin annoys me. I think both AucTeX for vim and Vim LaTeX-box, but to each their own. They all have their own methods for dealing with errors.
Best Answer
For LaTeX, use the commands described in section 4.9 of
clsguide.pdf:\PackageWarningand\PackageWarningNoLineif you are writing a package\ClassWarningand\ClassWarningNoLineif you are writing a class\GenericWarningThe
expl3bundle has another interface for warnings and similar messages, see Part III, chapter 11 insource3.pdf.