I think there's three clips on either side, but it's not them that have a tendency to break, it's the actual heat shield itself that is weak where the mounting holes have been drilled. Unfortunately it's a common problem.
The millie's broke on the passenger side on the way up to Scotland a few months back, and we just sort of bent it back up so it wasn't dragging or catching on anything. It was only a temporary solution though, as the extra stress on the other side caused that to break too. Dal had a look at a temporary fix with some hand crafted brackets, but it was beyond repair as it had broken at all six of the mounting points. So he took it off.
It shouldn't do any damage to a standard car. As Dal's got a Milltek, it's a bit closer to the brake lines in places, so he needs the heatshield on his. I managed to completely rip the heatshield off my old XR3i, and was driving around with the replacement in my boot for about six months with no lasting damage.
They're not exactly expensive to replace either, so get a replacement when you can be bothered, and replace it when you next need something doing to the car!
Conclusion: if it's standard, don't worry about it.
