I ran ssllabs.com test for browser Opera Mini 11.0.1912.96480 and it tells me that the browser is vulnerable to LOGJAM, FREAK and POODLE (SSLv3) and tells me to upgrade my browser as soon as possible. However I am using the latest version from Google Play, so this seems to be serious issue with Opera Mini itself.
Another issue that it warns about is Opera Mini acccepting all mixed content. It's widely accepted behaviour to only accept images which are passive content and this is what you see with all major desktop browsers (including Opera). The test also warns about supporting insecure ciphers and not having OCSP stapling.
Android 4.4.4 on Samsung GT-I9305.