The point is that it works even if there is only one electron travelling through the apparatus at one during the time t takes for the electron to be emitted until it is detected after passing through the slits.

This quantum mechanical weirdness does seem to cause lots of people problems but the behaviours are completely proved. however there are hopes for those who must have a more rational explanation of things. this problem is sometimes called the EPR problem after the people who first posed it Einstein Podolsky and Rosen

The critical work by Bell that clearly proved that quantum mechanics could not be explained by hidden variables had a limitation this was that the variables were subject to the normal rules of arithmetic. Now this may not always be the case

If for example the variables were non commutative there could be hidden variables a non commutative process is one in which the order in which you do things is critical so if you do A then B to something that is not the same as doing B then A a good example of this is doing a 90 degree rotation in one dimension on an asymmetrical object like a book.

A fuller report is given in the New Scientist 3rd November pages 36 - 39

The original paper is in

http://www.arxiv.org/abs/quant-ph/0703179