I think it is meant to be an interesting clock, not a good clock in the timekeeping sense. There are many times that do not have an associated quote, so the time it shows if often off by several minutes.
If you just need a good clock, https://time.is/ is hard to beat.
I think it would be interesting to, say, look at the clock just before 5 PM, as I'm getting ready to knock off work and find something fun to do, to be told that it is five minutes to midnight at Hogwarts and Dumbledore is advising Hermione that three turns should do it.
I think it still wants to be a useful clock, i.e., you want to be able to see at a glance how late it is where you are now. That's actually why the current time is highlighted.
