This is probably a candidate for ServerFault.com since all your application services are running way above the underlying transport protocol.
Ideally, you shouldn't have to change anything within the application. I say ideally because my own apps (i.e. code I have specifically written) use the IP address in some places to identify internal connections. This'd have to change - but this is specific to my app.
As long as you can ping the server(s) by IP and by name from your client machines, everything else should be expected to work since names are being resolved and packets are being routed. The IP stack will decode the payload and pass it up to whatever service is listening.
The only caveat is that IPv6 addresses have a lot of colons, so check the browsers can make sense of addresses such as this:
_HTTP://[ 2001:0ff8:0000:0000:0000:0000:1986:69af]:80/
The browser should notice that the IP address is in [] brackets and work as usual, but older browsers might fall down.
Any issues you get would make an interesting blog post.
Good luck
Luke
(_HTTP to stop stackoverflow getting confused)
UPDATE:
Adding IIS6 IPv6 issues list link:
http://www.microsoft.com/technet/prodtechnol/WindowsServer2003/Library/IIS/4c7c6bce-213a-4125-bc36-2202e3b4c8c8.mspx?mfr=true