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http://www.sacbee.com/2012/07/22/4648658/spending-smart-its-important-to.html
Errors on your credit reports might mean you could be denied credit or be offered higher interest rates than you should be. They could also mean you'll pay more for auto insurance or be denied a new job. But even if you're diligent about checking your reports and find a mistake, it can be a nightmare to correct it. It helps to know the proper steps to take.

http://www.startribune.com/lifestyle/162274516.html?refer=y
Unfortunately at the time I did not realize the mistake, and I booked a nonrefundable room in the wrong London.

- find a mistake
- realize a mistake
What is the difference in meaning between these two?
Comments  
To find a mistake is to discover or spot one. For instance, I find many mistakes on this forum.

In the StarTribune sentence, what the writer meant by I did not realize the mistake was that he hadn't been aware of his own mistake until it was too late (booking a room in the UK).
Find a mistake - another person made the mistake and you found it.
Realize a mistake - you made a mistake and you found it.
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AlpheccaStarsFind a mistake - another person made the mistake and you found it.
The phrase needn't be limited that way. One can find mistakes in his own work, such as typos, misspellings, miscalculations, etc., as after proofreading or reviewing.
AlpheccaStarsRealize a mistake - you made a mistake and you found it.
I don't think we commonly 'realise a mistake' in British English.

We can realise the mistake, recognise that a mistake has been made by ourselves or by somebody else, and we can realise (that) a mistake has been made.
Aspara GusOne can find mistakes in his own work
I agree with the thought, but note that this would need to be One can find mistakes in one's own work in British English. Anether AmE/BrE difference to add to the collection.
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Aspara Gus AlpheccaStarsFind a mistake - another person made the mistake and you found it.The phrase needn't be limited that way. One can find mistakes in his own work, such as typos, misspellings, miscalculations, etc., as after proofreading or reviewing.
That's right. You really have to look for the mistakes to find them. Sometimes it can be difficult to find your own mistakes.

Realizing your mistake is understanding that you made a mistake without consciously or diligently looking for it. It's a kind of an "oops" moment.

I need to get fit, so I have made a decision. I do more exercise