I'm calling pdflatex from within my (C++) program using system(), needless to say all the garbage pdflatex puts on screen is a bit irritating in this case.
So...how do I encourage pdflatex to forego the lengthy outputs? It would be even better if only errors would be visible...
To simply ignore all output, redirect pdflatex stdout to /dev/null:
system("pdflatex yourdocument >/dev/null");
You may want to add \nonstopmode at the beginning of your document to instruct tex to keep going even when encountering errors.
To get the error messages, pipe pdflatex output to your program and look for errors around rows starting with !, e.g.
FILE *outputf = popen("pdflatex yourdocument", "r");
// ... read and analyze output from outputf ...
pclose(outputf);
Unfortunately (La)TeX doesn't really abide by the rules of stdout and sterr, owing (I assume) to its origins in the early 80s. But there are some switches you can invoke to alter the amount of information being shown.
Execute latex with either the -interaction=nonstopmode or -interaction=batchmode switches for non-halting behaviour even in the case of a syntax error. nonstopmode will print all usual lines, it just won't stop. batchmode will suppress all but a handful of declarative lines ("this is pdfTeX v3.14...").
These can also be invoked from within the document with \batchmode and \nonstopmode, but this is less useful for the situation you're describing.