I had the similar problem but i found the solution. Adblock extension is the culprit for this problem. Disable the adblock and check the resolution.
1. Disable adblock
2. Close the browser
3. Open the browser
4. Check youtube video resolution
5. If it works than enable the adblock extension
This is the exact problem i had.
http://my.opera.com/community/forums/topic.dml?id=1802212
Hope it works for you.