“working with a site” and a site being build to web standards are two VERY different things.
Opera adheres to Web Standards, and if you write your website to those web standards, it will work just fine in Opera, it will also work just fine in Opera Mobile, and any other browser than strictly adheres to web standards.
Chrome, Firefox, Safari and IE are mostly web standards compliant, but have many browser specific quirks, when you see a site working in Chrome and not in Opera, a simpleton might come to the conclusion it’s the browser, however the reality is the site was written poorly and hacked to work with specific browsers.
For badly written major websites, Opera fixes their code for them, on-the-fly using Browser,js, which modifes the website when you visit it, to fix all the coding errors and make it work as it should.
http://my.opera.com/core/blog/show.dml/3130540
http://my.opera.com/sitepatching/blog/
Whilst it’s mostly patching to fix web standards and poorly coded sites, it does also from time to time work around Opera bugs, however once the bugs get fixed in Opera, the patches get revoked.