Okay, here are several more ideas I had:
1) The judge has another 3x3 with gray stickers only. When the competitor is done memorizing he trades cubes with the judge, and solves it. The judge should watch very carefully to see what the competitor is doing, and do the exact same turns on his (real) cube, but be careful to keep the cube he is using out of the competitor's field of vision. The solve is successful if the judge's cube is solved when the timer is stopped. Cheating should be impossible if the judge is competent (of course we assume the judges are trustworthy).
2) During the round, the competition organizers project something interesting onto the ceiling (such as a compilation of sub-10 3x3x3 solves). Each competitor who solves blindfolded will be required to stare at the ceiling throughout the solve. The judge makes sure that they do not look downwards in any way. Cheating is only possible if the competitor has excellent peripheral vision.
3) The competitor can use a normal blindfold, but after the solve the competitor must tell the judge (without looking at the cube) what cycles were necessary to solve the cube. If the judge cannot verify that these cycles will in fact solve the cube, or the competitor does not remember the cycles, the competitor is considered to have cheated and the solve is a DNF. Cheating would be difficult because the competitor would still have to remember the blindfold cycles when the solve is finished, so that someone who is incapable of a normal blindfold solve would not be able to get a decent time by cheating.
4) Before the round, the competitors should prepare a few clean black plastic bags (such as garbage bags), preferably with a few small holes in them. Instead of a blindfold, competitors place these bags over their heads, and loosely tie them at the neck to make sure they cannot see out. If a competitor becomes unconscious during a solve that solve is considered to be a DNF. Here cheating is only possible if the holes are too big (assuming there are holes at all).
5) Instead of physical cubes, competitors solve virtual reality cubes. Once a competitor has donned the virtual reality helmet and gloves, they may begin the solve by starting to look at the cube. As soon as they indicate they are ready to start the solve, the cube's stickers all turn grey in the virtual reality simulation (like on the Ryan Heise blindfold applet), and they must then solve it and stop the timer without knowing what any of the stickers are. I don't think there is any way to cheat with this method.
6) Regulations require all competitors to bring a clone of themselves to the competition, but the clone may not know how to solve the cube. When the competitor has finished memorizing, the competitor hands the cube to the clone, and they stand back to back. The competitor then tells the clone what turns to make to solve the cube, and the solve is completed if the clone's cube is solved when the timer is stopped. Ideally the clone should be blindfolded, and also not allowed to talk. Cheating is only possible if the clone can in fact solve a cube, but this should be easy to detect.
7) Before the blindfolded round, all competitors are made to sign a legally binding contract which states that they agree to be punished if they cheat. Normal blindfolds are used during the round. Afterwards, any competitor who is found to have cheated will be taken to the Rubik's Cube factory to be made into new DIYs.
8) I call this one the "youtube approach". Competitors can solve with whatever blindfold or method of concealing the cube that they want. However, if anyone in the audience thinks they see a way that that competitor could have cheated, and yells "fake", the solve is considered to be fake and is counted as a DNF.
9) Only blind competitors may compete in a blindfold event. Before the round both a blindman's cube (with raised shapes to signify color) and a normal cube are scrambled in the same way. Once a competitor has memorized the cube, they switch with the normal cube, and solve it. Cheating will only be possible if competitors pretend to be blind.
10) Each competitor does their blindfold solve in a small room with a video-camera (with infrared vision) and a separately operable light. When they are finished memorizing the cube, a judge turns the light in their room off, and they must complete the solve in the dark. The light turns on again when they stop the timer. Cheating may be possible if competitors have some other way of creating light in the room, but ideally they should be carefully searched beforehand.
I'm just kidding of course, wanted to have a bit of fun with it
I think that we should not worry so much about cheating, as I think Stefan has showed that anyone who is found to have cheated during a competition will lose all respect in the community and probably end up banned from future competitions. Anyone who is actually interested in cubing would make sure to avoid cheating since they don't want to lose all respect.
......First competitors are allowed to inspect the cube in a normal fashion. When inspection is completed, a plastic surgeon will surgically remove both of the competitors eyes. The solve is preformed eyeless until the stackmat is stopped. This method has the advantage of being virtually impossible to cheat, but there are always ways...
