I'm doing a course on this at the moment. The figures given are that there is a copying error for one base pair in every 10 to the power of 10. The human genome has around 3 * 10 to the power of 9 base pairs so there will be a mistake in about one in every three cell divisions. As Mrrzy says, most DNA doesn't code for anything so there will be far less errors in actual coding DNA.

As Keith says, that 3% isn't about the chance of making copying errors, it's about the chance of inheriting genes that have already been miscopied, possibly generations before, but have survived in the population because they are recessive.