Well, at least for some, the ‘nannyware’/security software interference is the answer.
The sudden onset, happening only on a specific site (or possibly sites with the same software) and the images breaking partway through loading (with an unspecified) error all indicate an infection, a bad update or a ‘security’ measure going ‘overboard’. Similar things used to happen all the time with various firewall apps (ZoneAlarm was particularly bad with this kind of thing).
In general, if it is not extremely widespread and not easily repeatable on other machines, it’s most likely a problem on the individual affected computers, as opposed to a site or server problem.