Hahaaaaa!!!! Sussed it out.

Looking at the screenshot does indicate that the clock is way out. But on further tinkering I've discovered that it's just not displaying the correct skin.

In the screenshot it should have been displaying the 24hr clock, as I had that enabled in the settings. Disabled 24hr and bingo! It now seems to be working fine.
Not sure about the disappearing widgets problem, but it hasn't happened again since, so I'll keep an eye on it.