It happened to me a few times that I installed a Windows PC after the CMOS battery has been replaced and all sorts of things stopped working or threw security warnings, only to realize that I just need to set the clock, or click on the sync button.
From the above experiences I deduced that time synchronization is important for security. Intuitively I feel like time synchronization is important, e.g. a certificate can be valid at a certain time, but revoked at a different time, but it's unclear how dangerous time missynchronization is.
If we consider the certificate example, I can imagine that the conversation between my browser and some certificate server goes like this
me: is this certificate legit right now (my current time: 1st of January 1970), cause I need to know if I can safely write my password on the bank's website? server: this certificate is not legit right now (by the way, the current time is 29th of November 2020).
From the above conversation we can see that we can figure out whether a certificate is legit "right now" by asking about its "right now" status, regardless of the absolute time associated with it, so regardless of how wrong my time is set.
So, what kind of vulnerabilities exist on a PC with a wrong time, but otherwise as safe as any other PC with an up to date windows, and perhaps some antivirus software?
Assume the PC is used in a typical scenario, say, an office with important documents, but still human operated. The PC in question is not the one operating nuclear attacks, nuclear reactors, anything with nuclear in its title, or anything that can be considered a gun, or a bomb.
There is a similar question asked, but it only deals with a hacker having access to setting the time on a PC, I am more asking of the dangers of just having a wrong time set, which is otherwise working correctly.