At DO they should be able to tell you if it's a mistake. You might want to go again and talk to a supervisor, as Joe suggested. It is up to you to have the date on your green card corrected, but you have to make sure to apply not earlier than 5years - 90 days from your CORRECT permanent residency start date.citizen2006 said:
There was a typo on my husband's green card - the day and month were right, but the year was 1998, instead of 1994. We got our plastic cards in 2002 only, and I was waiting for them because I wasn't sure what date will they put on our green cards. So, it was 1994 (the POE), and I filed N-400 for me and my elder daughter. As for my husband, I waited a few more months until 2003, and only then filed N-400, even though it was an obvious mistake on his green card. I just did not want to take any chances.