Frido mentioned to me that there seems to be an issue with Multisite if you use both http and https sites. The issue occurs when you do a network upgrade. The following message appears:
Warning! Problem updating https://nonsecureddomain.com. Your server may not be able to connect to sites running on it. Error message: SSL: no alternative certificate subject name matches target host name 'nonsecureddomain.com'
This appears to be a WordPress bug, as discussed on StackExchange, and was posted as a bug: