No. Also, I didn't encounter this problem on any other website with support for google login.

When I try to login to SO with the connected Google account, I always get an error message, saying:

=============================================
We've detected a problem with your cookie settings.

Enable cookies
Make sure your cookies are enabled. To enable cookies, follow these browser-specific instructions.

Clear cache and cookies
If you have cookies enabled but are still having trouble, clear your browser's cache and cookies.

Adjust your privacy settings
If clearing your cache and cookies doesn't resolve the problem, try adjusting your browser's privacy settings. If your settings are on high, manually add www.google.com to your list of allowed sites. Learn more

But my GMail or anything else is working fine. Is there a problem with SO / Opera? (I'm using the newes version.)

Recently I bought an Galaxy Note Tablet. A feature that I really like about it, is the possibility to use two Apps at the same time (Two Windows). But this doesn't work with all Apps. And unfortunatly it's not working with Opera. So, it would be really great if you could implement this feature.
Maybe you have to use a certain API from Samsung, but I guess this might not be too hard...