How do I know whether the incorrect information on my green card was caused by a USCIS error or my mistake?

Support your claim with evidence.

According to the USCIS if the information you sent in your application does not match the information on your green card, the mistake may have been due to a USCIS error. You should send in any evidence to support your claim when requesting a replacement green card. CITATION: Page 6. 3d.; http://www.uscis.gov/sites/default/files/files/form/i-90instr.pdf