If the mistakes are not important, it could be easily explained by the police (knowing your state at that time) and may not do anything, but if the mistake are significant which may considered as lying to deceive, this will not be taken lightly and will be held against you in court. So it better to talk to the police and get all the facts correct and accurate so it does not backfire on you. I am not able to say about your situation as I don't know what your mistakes are, you are the only one who can decide.
