<p>What kind of multi-threading issues do you have to be careful for in asp.net?  </p>

Programmatic Caching is one area which immediately comes to my mind. It is a great feature which needs to be used carefully. Since it is shared across requests, you have to put locks around it before updating it.
Another place I would check is any code accessing filesystem like writing to log files. If one request has a read-write lock on a file, other concurrent requests will error out if not handled properly.