I painted the minimum date of the Power of Attorney for Patent with correction tape, and changed the date of 12 to 2. Can the Patent Office handle cases normally?

It doesn't matter if this slightly later time is also before the patent application date; Otherwise, there may be amendments.

However, you don't have to worry too much. If the Patent Office doesn't accept it, it will send a correction notice and ask for a new power of attorney. If it is not notified, it will be accepted.