Anticipating Problems
You can correct a mistake after the fact, but, oh, what a wearying chore that is. The easiest way to deal with mistakes is not to make them. You certainly are going to make your share, but you should also avoid more than your share. Some presence of mind and preparation can go a long way to reducing time, money, and energy
Do Some Research
One way to avoid a mistake before it happens is to work with information and not out of ignorance. If your team is going to undertake a task, the members should be doing basic research. How have people successfully solved the problem or similar problems in the past? In what ways does what you are trying to achieve differ from what others have done? What are the requirements of the customers (again remembering to use the term broadly)? Do you know the organization's expectations? Are there reference books or experts that you can draw upon for insight? The research process is really one of directed questioning. Assume that you don't know the answers ahead of time and find out what others with experience think.
Avoid Rationalization
Learning alone won't keep you from all errors, and some of the dandiest you can commit involve the misapplication of what you've learned. One of the biggest is rationalization. Often, particularly in a corporate setting, people for some reason decide on what they want to do and then look for justification. The reason to do research is to increase understanding, not create something to blame.
The surest sign you're going down a blind alley and into a brick wall is if you start looking for statistics as proof of a position without spending the time to understand what the numbers actually mean — which is often different from how someone presents them.
There is a variation on this, in which people effectively create rationalizations though blind assumptions. Instead of having someone tell them to concoct an excuse for a decision, they operate under beliefs without testing their validity. That is an extreme form of rationalization: the assumption of infallibility. That's a grand way to make horrendous mistakes.
Remember Your Experiences
You've made mistakes before, so use your experience. Look forward to similar situations to avoid future problems. The result is like a form of time travel. Your imagination builds a picture of what could happen, based on your experience. Knowing what can land you in that situation lets you make plans to avoid it. In a fanciful sense, you see the future and come back to tell yourself how not to wind up there.
A simple example is locking yourself out of your car with the key in the ignition. You could do this time and time again, but why should you? Knowing that you have the propensity for forgetful behavior, you might choose a number of actions that would keep you from the same situation. You might train yourself to only lock the door from the outside with the key, rather than locking the door before you close it. Another solution would be to keep a spare key hidden in a magnetic container under the car or slipped into your wallet. Alternately, you could get a car with a combination lock or a car that recognizes when you've left the key inside and won't lock until you retrieve it.

