Using Opera's built in "Mask as Firefox", which completely changes Opera's user agent string will in fact not fix the problem. You will need something which completely hides Opera from the server. I am using Proxomitron combined with Andrew Gregory's custom config file for faking browser IDs.
So even if a site is still broken when masking as Firefox, the site could actually be digging a lot deeper to identify the browser. If you want to be absolutely sure that it is not a bug in Opera, you may want to use a local proxy which rewrites HTTP requests on the fly to make sure that the server isn't doing anything it shouldn't.
To this day, browser discrimination remains probably Opera's main compatibility problem. If only sites could at least send what they are sending to Firefox, a lot of more sites would start working.