<p>Usually, we install VS.NET on our production server, to solve problems easily with our product, if necessary. </p>

<p>Is this a good or bad idea?</p>

Both.  One of the upsides is that it can sometimes make diagnosing problems easier.  One of the downsides is that sometimes the install can break a working web application.  I would only do it if I had to.
Edit: another potential downside to this occurs when a co-worker decides to debug a live process on the production server, stops the app on a breakpoint, and then goes to bed without realizing he has left the app unavailable.  Yes, this has happened to me.