My own site has been fully SSL for a while now but I noticed a security error while viewing it on my Android phone using the Chrome browser recently. It’s fine on a desktop. I googled around a bit and contacted my SSL issuer NameCheap.com for advice and they suggested that I hadn’t installed the Certificate Authority (CA) bundle while installing the main SSL cert initially. The CA bundle is optional when installing an SSL cert but it exists to improve compatibility with web browsers and clients so is worthwhile putting in too.
NameCheap provided the CA bundle code via email and it was a fairly straightforward process to go in to my hosts Cpanel and add the CA to the existing cert via the SSL/TLS Manager.
The process is outlined here:
Namecheap.com/support/knowledgebase/article.aspx/9418/0/cpanel