Examples of good responses include:
1. I think one of the most important things I've learned is persistence. Not to give up too soon, because the solution is probably right in front of me.
2. I have learned to give every person a second chance, because first impressions can often be misleading.
3. I used to think that there was one best solution to a problem, but I've learned that that kind of thinking limits the possibility of great success.
Everyone makes mistakes. It happens. It's fine to share your mistakes during an interview as long as you are clear that you have learned from it. However, it's a good idea to not mention a mistake that would be critical for success in the new position.
If you're asked to give an example of a mistake that you have learned from, give an example from your last position that isn't specifically related to the job requirements for the new position. It's also a good idea to mention something that is relatively minor.
Explain, as well, what you learned from the mistake and what you did to ensure it won't happen again.