1) No contact info. This is the worst offense of all. You can have a website that looks great and has tons of great stuff about the band, but it will all be for nothing if people can't reach out and touch you. This means they can't send you an email to book you for a gig, to ask you to exchange links, to become your fan, to buy something, or to complain about something. Music 3.0 is all about communication with your tribe, so displaying your contact info so it's easy to find is job #1.
2) No mailing list registration. If you don't have a mailing list, now is the time to create one. It's the main way to reach out to your tribe. Consider it your marketing arm for telling your fans when you have a new release or when and where you'll be gigging. Make this really obvious because it's one of the main reasons for having your own website. Check out this previous post for more info on mailing lists.
3) No easy way to purchase your music. It has to be both obvious and easy to buy one of your tunes or CD's. Don't make someone go find it. Either sell it directly from your site or have a direct link to iTunes, Amazon, CDBaby or any other distributor you're using. Make sure you go through the process yourself to make sure the process is completely easy and seamless.
4) Too much information. Don't make the pages of your site so loaded with photos and text that they're difficult to read. Try to keep the text down to 300 to 400 words, and make sure there's a lot of white space. Check out some of the artists and bands you really like for ideas.
5) Bad links. Everyone hates bad links. Your fans will loose interest and Google will penalize you in the search engine rankings. That's why it's important that every link works on your site, and every incoming link to your site work as well (which is a given, because you won't even have visitors if the links are bad to begin with). Consider the "Error 404 Not Found" prompt as the worst thing that can happen on your site.
6) Bad email address. Almost as bad as a bad link is a bad email address that bounces. Fans find this very disrespectful. Sending them to an email address that you never check is almost as bad. Make sure that the address works and is forwarded to the address that you check every day. Make sure you answer any email within 24 hours.
7) No Press section. While not having a press section on your site is not fatal, having one is a sign of professionalism and will be a big help to anyone trying to book you or write about you. See this previous post for more about what your website press section should be.
These are mistakes that usually result from not giving your site enough attention in the first place. They're easy to correct and totally necessary to avoid in order to maintain and build your tribe, and facilitate any marketing and sales efforts.
Check out my Big Picture blog for discussion on common music, engineering and production tips and tricks.