Microsoft doesn't really keep a public list of open bugs. The ones that are the most important (e.g. anything involving security) are kept private for obvious reasons - they actually aren't published until they are fixed (and even then they often remain private). Not that there have been many security issues with SQL Server in the past 12 years, but by necessity, we don't know what we don't know.
And to be honest keeping such a list out in the open would be like BMW keeping a bulletin board with all the problems that still exist on their 2006 M3. It's kind of like a dirty laundry list, and other than satisfying customers who refuse to upgrade to more modern (and arguably "more fixed") versions, what would it do for them? :-)
Now, you could go out to http://connect.microsoft.com/sql/ and peruse the list of bugs opened against SQL Server 2005 that are still open. But that wouldn't be the whole story, since many bugs were opened against 2005, then closed as fixed when the fix was actually implemented in a more modern version. Never mind the large number that were closed as by design or not reproducible but that still affect you to this day.
You could also go to the knowledge base http://support.microsoft.com/kb and try to find all of the issues listed there that haven't been updated to include the text "this issue has been fixed in [such and such update]." This would also be a Herculean task that I would not wish against my worst enemies.
In the end, if you are not affected by bugs you do not know about, they may as well not exist, right? And if you are continuing active development against SQL Server 2005 and you come across an issue, it is highly, highly unlikely that you will be the first person to come across it. So if you come here for assistance you will stand a very good chance at getting the guidance you need - either a workaround to get around the bug by coding the query a different way, or a trace flag, query hint, or a completely different approach.
I know this isn't the answer you're looking for, but I'm quite afraid you're not going to get the answer you're looking for. This answer (and this site, to be honest) is quite possibly the next best thing. When you have a specific issue, bring it here, and we will help.