Correction of errors in military registration

I read the news that a man was mistakenly added to the database of wanted conscripts due to a bureaucratic error. This scares me a bit, as I don't understand what to do if I also find myself in such a situation due to incorrect data at the military recruitment office. What are my actions to quickly correct such an error and remove myself from the wanted list? Is there a way to prove that it's not my fault, and will I bear any responsibility for this?