A conviction can be appealed on a number of grounds. One way of looking at it is that convictions (and civil cases) can be appealed based on an error of the law or an error in the facts. In some cases, factual errors are hard to gauge, as a reasonable jury might have decided the facts either way. In others, however, a factual error is a straightforward mistake, such as a mistake in math or a wrong date. This is called "plain error."