That error means that your server configuration isn't setup correctly to properly request and read an SSL certificate. We do have an option to skip some SSL checks in Facebook, but that's for a very specific case, and can't be done generically across all social network providers.
I'd recommend contacting your hosting provider and making sure that the certificate bundles are setup correctly. Specifically, your server should be able to make an outgoing request to
api.twitter.com/ .
I hope that helps get you started. If not, let me know. We can look into if there are other ways to work around the SSL checks, but it's not recommended. Those checks are there for a reason, to make sure that your site is really connecting with Twitter.com and not some other site that's masquerading as them. If the SSL checks are disabled, privacy and security becomes an issue.
Thanks,
Alex