In addition to hippo's point about discriminating 13-digit serial numbers by month and year, assume that a check digit is present and check the check digit against the ever-present serial number. You then have a 9-in-10 (update: well, assuming the check digit is in the range 0..9; there are other possibilities) chance of detecting the absence of a check digit (i.e., the assumed serial number does not match the assumed check digit), and this will let you make a better guess (but still only a guess) about which format of 13-digit serial number is present.

What is the method for calculating the check digit? Also, are the month numbers 0 .. 11 or 1 .. 12?