I'll be the first to admit that I'm not thrilled with the mobile version of my site, but then again I'm not thrilled with the full version of my site--it's just a WordPress blog that I keep tweaking to suit my needs. It's a huge step up from the site I inherited when I started here, though, which was really just a collection of links on a school website that looked like it was stuck in a mid-nineties time loop (as so many educational sites, unfortunately, do; ours has thankfully gotten a facelift since then).
I don't have much control over my mobile site right now because I don't host my own site or do much of my own coding--I use a WordPress template, although I do a lot with widgets and pages--but I do take a look at our site on my phone from time to time to see if WordPress has made any changes to the mobile version, and make sure mobile visitors still have access to the features they need. And what do they need?
I think a lot of librarians worry about mobile sites that don't include all the features of their full website, but mobile users aren't always looking for the same functionality that they want when viewing a site on a larger tablet, laptop or desktop. (Just look at apps for websites like Yelp! or IMDB.) This is where it's important to know what your teens need when they're trying to view your website from mobile devices. Do they want to browse your catalog? Do they need access to your databases? Are they looking for a calendar of programs and events, or do they just want to know how late the library is open on Thursdays?
One shortcoming of my mobile site right now is that it doesn't include the sidebar, where a link to the OPAC ordinarily lives. Atriuum just launched a pretty great new mobile version of the catalog (although the Scan Item option at the bottom dead-ends to an error page right now--and I had such high hopes for inventory!), but it doesn't do my teens any good if they can't find it from the library homepage.
Take a look at your library's mobile version. Can you search for books? What about e-books? Can you make requests or write reviews? Can you access a database? Could you find hours of operation or contact information for the library? Does the color scheme singe your eyeballs?
If you have a mobile site that you really love, leave us the link in comments!