There are no adverse effects that should be associated with removing the heat shield, but I would think about getting it fixed before removing it completely. Any muffler shop should be able to spot weld it where ever the bolts have rusted through to get rid of that annoying rattle. If removing it is the only option, then I would just be careful of where you park it. Definitely not in a grassy area especially if the grass is dead or there is a lot of brush, sticks, pine straw, etc. Without that heat shield, you would most definitely start a fire in a grassy area.
The heat shield is used to diffuse heat as well as act as a barrier between the extremely hot CAT and any material (ex.grass) under the vehicle which might catch fire. In this respect it may be viewed as a safety item. I would not wish to be the owner of a vehicle which having caught fire, attempted to explain to the insurance carrier why I removed the shielding....guess what the insurance carrier's response would be???