The SCA also discourages (or disallows, I'm not sure which) the use of existing heraldry from the real world. That is, you shouldn't use your own family's arms.
Getting it to pass is also a challenge from the standpoint of uniqueness. If it too closely resembles other already-registered arms, then it won't pass. They require at least two points of difference from all other arms, if I recall correctly.
Simple is better, but some of the simplest arms are also difficult because they may resemble something else too closely. For instance, even if you use a bird that no one else is using, most birds can look the same from a distance, so if the colors and positioning match, it might still not pass.
Generally speaking, if you want to register your arms, you should get it passed before painting it on anything.
In terms of them disallowing your use of heraldry that is not passed-- Obviously they can't stop you from painting shields, or using it at non-SCA events. But they will probably enforce it if you try to use that heraldry in an official tournament. Beyond that, I'm not sure.
