I found a related TechNet Blog that shed some light on the subject:
Http://blogs.technet.com/b/tune_in_to_windows_intune/archive/2013/11/13/replace-certificates-on-adfs-3-0.aspx
According to this document, after setting the Service Communications Certificate in the MMC, you must run:
Get-ADFSCertificate
To fetch the certificate thumbprint of the Service Communications Cert. Take note of the certificate thumbprint and then run:
Set-ADFSSslCertificate -Thumbprint [yourThumbprint]
"Set-adfssslcertificate" would fix the HTTP. SYS bindings used by ADFS. Apparently the MMC does not set the bindings, which are pretty annoying because this leaves the service in a Prett Y darn broken state. The HTTP bindings is mentioned in this TechNet documentation:
Https://technet.microsoft.com/en-us/library/dn781428.aspx
But, the docs does not explicitly state and the Set-adfssslcertificate cmdlet needs to being run on all of the ADFS server Nodes in your farm. This also is a key missing detail.
CRM Security Certificate Expiry action command