Opera Mini is a smaller version of the Opera web browser designed primarily for cell phones. Opera Mini allows you to do on your phone what you can do on your computer. The "Verification of server certificate failed" error is due to the date settings being set wrong on your phone. If correcting the settings does not fix the problem, downloading Opera Mini again takes care of it. The "Verification of server certificate failed" error seems to happen more on Nokia cell phones than any other.
Check the date on your phone and make sure it is correct.
Check the Date/Time setting on your phone to make sure it is set to "Update from Network." You will more than likely find this setting under "Options" on your cell phone.
Turn your phone off and then back on.
Download Opera Mini (see Resources) again if the above steps did not fix your problem. Navigate to the website on your phone. Click the "Opera for Phones" download button and follow the onscreen instructions to install it on your cell phone. If you cannot navigate to the website on your phone, you can download it on your computer and transfer it to your phone.