As an Austrian; thank you for bringing this up. People from other countries are often confused or concerned about this law, so I'd like to clear a few things up. The situation is very similar in Germany, but since I'm an Austrian, and you specifically mentioned the Irving trial, I'll concentrate on that.
The Verbotsgesetz is indeed an intentional limitation on free speech. As far as I know, this is the only major difference to what is considered free speech in the US, although we may be a bit stricter concerning incitement of popular hatred against ethnic groups. Both the Verbotsgesetz and the right to free speech are part of the Austrian constitution. To understand why we have this law, and why such an obvious limitation on what we can say or publish is tolerated by the people, you need to take a look at when and why the law was instated.
The first version became law on May 8, 1945 - the very day that WWII ended in Europe with the capitulation of the Wehrmacht. Its main and largest part deals with the process of "denazification," which was an acute necessity in order to resume normal life after the war. It was also mandated by the allied forces, who continued to occupy Austria for the next ten years. This part is now dead law, because the denazification is as complete as it's ever going to be, and also because there was an amnesty for former members of the NSDAP in 1957.
The second part of the law forbids the reformation of the NSDAP and certain organizations associated with it (like the SS, SA, etc). It also - and here's where the interesting part comes in - made national-socialist activities illegal. This includes any action which "denies, belittles, condones or tries to justify the Nazi genocide or other Nazi crimes against humanity".
I'm sure you will understand why such a law was considered necessary immediately after the war. So why didn't we repeal it later? The main reason for that was to send a strong public signal that this era is once and for all over. During the time of the Third Reich, there was a significant brain drain in Germany and Austria. Many of the most important scientific minds, as well as writers, artists, lawyers, doctors, etc, were Jewish and were forced to emigrate. It was of great importance to prove to those people that it was safe to return.
Which leaves the question: how long should this law, as a special case due to historic necessity, remain in force? This point is actually debated regularly, but unfortunately the only people who are publicly advocating to repeal it are from the extreme right. They're not at all concerned about freedom of speech in general, they just want to avoid fines and prison terms after their typical antisemitic tirades. As a result, they are consistently voted down. As for me.. as long as there are Holocaust survivors living in this country, I wouldn't want the law repealed. At some point in the future, it would probably be best to put it behind us and let the normal laws handle these cases.
By the way, this Innocence of Muslims video (idiotic as it is) would not have violated any Austrian law. There's no need to be afraid about speaking your mind in Austria, as long as you don't publicly deny or condone the Nazi war crimes. Irving knew that perfectly well. He knowingly violated the Verbotsgesetz multiple times, and as a result he had to spend 13 months in prison. It was a stupid thing to do, and it appears he has learned his lesson.
CJ