I had a friend adjust the handbrake on my car, he's a brake specialist. To do it, he removed the exhaust heatshield, and didn't bother to replace it.
Since then my exhaust rattles a little (not loads but audibly noticeable) on idle and a little more when the car is under load.
I'm not too bothered about it, when the windows are up it's hardly noticeable.
But the MOT is due in a couple of months, will it fail if the exhaust rattles, and is there any problem in not having the heat shield on there?