I live in Virginia and I started a new job in DC. After my second paycheck (since I never got a first one) I noticed that my employer was witholding taxes for DC instead of Virginia. I contacted them and asked them to change it and fix the problem retroactively since I did not want to file for DC (I am already filing for VA, MD and IA). They told me there was nothing they could do (even when it was their mistake) and that now I had no choice but to file DC too. I believe that to be incorrect. They could have fixed the problem before Dec 30. Am I right? Where can I find information regarding this? Thanks.

It is not your choice. Income earned in DC must be reported on the DC tax return.
You will also report this income on your resident state tax return. On this return you will claim credit for taxes paid to DC.
Read: Your U.S. Tax Return: Working or Living in Two or More states (http://taxipay.blogspot.com/2008/06/working-in-two-or-more-states.html)

MukatA is correct that you must report the DC-sourced income on your resident state tax return.

However, DC is unique among the taxing authorities in the U.S. as they do NOT tax income earned by non-DC residents in the DC area. Only DC residents must pay DC income taxes.

Hence, when you file your DC return (it appears you have no choice if your employer refuses to fix the withholding problem), you will get ALL of the withheld DC income taxes back as a refund.