Senga,
I am in the same boat. My physical GC has error on the resident date. It should say 2004 and the card came with resident since 05. I had no idea that it was wrong until when I went to the local USCIS office to apply for travel document. I was told to correct the GC by sending it to the service center it came from. The form you should use is I-90 option D. You should include a cover letter indicating that the error was caused by USCIS administrative error.
I hope that helps.
Bill