Wanted to highlight what I think has been a very useful discussion in the comments, because I know many readers don’t read the comments.
Yesterday, Brian noted that mistakes are inevitable in science (it’s a great post, BTW-go read it if you haven’t yet). Which raises the question of how hard to work to prevent mistakes, and correct them when they occur. After all, there’s no free lunch; opportunity costs are ubiquitous. Time, money, and effort you spend checking for and correcting errors is time, money, and effort you could spend doing something else.* I asked this question in the comments, and Brian quite sensibly replied that the more serious the consequences of an error, the more important it is to prevent it:
Certainly in the software engineering world it is widely recognized that it is a lot of work to eliminate errors and that there are trade-offs. If it is the program running a pace-maker it is expected to do just about everything to eliminate errors. But for more mundane programs (e.g. OS X, Word) it is recognized that perfection is too costly.
Which raises the sobering thought that the vast majority of errors in scientific papers aren’t worth putting any effort into detecting or correcting. At least, not any more effort than we already put in. From another comment of mine: