Physical Danger
You know what they say: the bigger the clock, the bigger the danger.
We don't actually think anyone says that, but it seems to be the case. If you're working on a wristwatch, you might have pinches or minor cuts to worry about, but nothing major. If you're fixing a clock the size of Big Ben, then we're talking a more hazardous work environment. Falling is the least of your worries; that big sucker has timekeeping pieces that could summarily crush a person into fine pancake form.
If you actually build the machinery from scratch, there's also the danger that comes with working with equipment intended to cut and shape metal―not exactly soft or forgiving for your hands.
If all you do is repair these babies, the hazards are limited and you should be fine. Seriously though, if you break your arm working on a Rolex, you need to seek a different profession. Probably something that involves lots of padding.