What drives new inventions? Demand. Check out this ad from Craigslist. I don’t think this poor guy will find what he’s looking for; it hasn’t been invented yet. But think of the money you could make off people like that — anybody, really, we all have regrets — if you had a time machine and didn’t mind messing with the course of history in order to help people who have done something stupid.
Unfortunately, the paradox here is that — assuming a single line of time a la Back to the Future, which you have to assume in order to help the actual person who is paying you, not just one of many versions of that person — as soon as the problem is fixed, he or she no longer has any reason to seek out your services. So you never get the money, because that individual never seeks you out. But because he or she never seeks you out, you never go back in time and fix the problem.
Anyone who has been watching Lost recently — mild spoilers ahead — knows that a more logical, or at least more emotionally satisfying, answer to the single-line-of-time time travel model is that you can go back, but you can’t change the past. So you could definitely find the one individual who needs your help and who has hired you to go back, but there is nothing you can do to help him or her.
Dude. I don’t get it.
Anyway, since a time machine hasn’t been invented yet (that we know of) one that comes along later would be of no help for those of us who have made mistakes in the past. The best theoretical models for how a “real” time machine would work insist that the farthest back in time a time traveler can go is the day the time machine was built. So if you build one, and then make a mistake next month, next year you can go back in time and try to fix it — probably with little luck (see above.)
I don’t know. As a business model, this is all looking pretty bleak.
Your best bet would probably be to abandon this single-line-of-time model and figure out a way to travel between parallel universes. Find a universe where you never made the mistake in question, kill that version of yourself, and take his or her place. Granted, this approach raises certain ethical issues.
Also, you’ll want to be very careful trying to kill that other version of yourself. Remember: he or she is smarter than you are, having never made the initial mistake.