In general, not every entry type (here: misc) supports every field (here: institution); the list of required and optional fields can be found in the bibtex documentation. If you need to change this, I would second the recommendation to switch to biblatex instead of hacking bibtex (although this might not be feasible if a deadline looms).
This does not address the question as posed, but here's a solution for the concrete problem: Since misc does not provide the institution field, I would just put that information into the howpublished field and select the plainurl (or abbrvurl, alphaurl, unsrturl) bibliographystyle. You also don't need the \url command, as this is automatically added.
@misc{Clason,
author = {Clason, Christian},
title = {{Numerische Mathematik I}},
howpublished = {Vorlesungsskript, Institut f\"ur Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universit\"at Graz},
url = {http://www.uni-graz.at/people/clason/teaching/numa12/NuMaSkript.pdf},
year = {2012}
}
The plainurl etc. styles also add the lastchecked field, which can be used to give the date when you last verified the page was there.
bibtex, the output is is governed by styles. In other words, it's the style you use that will determine which fields will be printed and which ones will be ommited. Another approach is to use thebiblatex/bibercombo instead.:)Just a note: if I'm not mistakeninstitutionis not available formiscentries. – Paulo Cereda Aug 1 '12 at 11:02