A couple years ago, my mom evidently listed me as a secondary user on
one of her credit cards. I think she was trying to do me a favor, by
making it so I could use the card if I ever needed to. She forgot to
tell me. Then she ran up $3,500 of debt on the card, and stopped
paying her bills. The credit card debt has now been referred to a
collection agency, and, among other things, is ruining my credit
rating, because my credit report says I have $3500 in unpaid credit
card debt, without making any mention of the fact that the debt is
actually my mother's. The credit agency says the only way to get the
card off of my credit report is by filing a police report stating that
I was fraudulently added to the card without my permission. This is
definitely *not* an acceptable solution. Is there any other way I can
get my credit report cleaned up?

The quick answer is probably no. But I'd suggest you look a little bit
into the consequences of filing a report with the police. I doubt that
they'd prosecute if no fraud was intended, and it's possible that the
statute of limitations has passed.

You should be able to write to the credit bureaus and have a comment
added to your credit report that you dispute the claim.  That may help
a little.  There is a service that I use to keep up to date on my
credit report and they have sample letters you can write and a ton of
other resources.  If you are interested email me and I'll send you a
link to them.  It costs about $15/mo

Actually, the truth is that the debt collection agency can NOT require
you to obtain a police report to honor your dispute.  They are
required by law to obtain validation of the debt from their client
upon receiving a written dispute from you.  Furthermore, if you were
placed on the account after it was open and are only listed as a
supplimental card holder, you do NOT have complete liability on the
account.  The fact is they can only hold you liable for any charges
you may have made.  There are federal laws which govern these types of
things.  I would recommend looking into the FCA and the FDCPA.  If you
continue to have problems with the original creditor or the collection
agency, file complaint with the Federal Trade Commission.  Also, you
have the right to dispute any item on your credit report.  If the
creditor can not provide proof of the debt (ie. a contract or your
signature) then the credit bureaus are required to remove it from your
credit.  Keep in mind the credit bureaus have to prove the debt is
valid within 30-days of receiving your dispute, otherwise it must be
removed from your credit.  I know this response is about 7 months
late, but if you still need help hopefully it answers your question.