I also have this problem with invalid certificate for Twitter. I'm running Opera 22.0.1471.70. I googled this and found that the problem is for a "Chrome client" running on Windows XP SP2. The recommended solution is to upgrade to SP3. Twitter is using a certificate that is not supported on SP2.
As Twitter is working with Opera 12.17.1863 and SP2, is it possible to remove the troublesome certificate in Opera 22?