Dear Zednought,
I'd like to thank you for your advice. I just do not know how to go about proving it was just a mistake. I am really planning to retain an Immigration Lawyer so he can advice me on this matter.
I would (somehow) try and obtain an official record from US Homeland Security about the events. I would have thought they
had some evidence that supported their claims that you had worked illegally in the United States. It would be my assumption
that it is this evidence that you need to demonstrate does not make you inadmissible to Canada, either because it is erroneous
or it does not make you indictable. To be honest I've no idea how you could go about this. Perhaps the best thing to do would
be to apply to your local CHC for rehabilitation and mark it for "information only". You would then get the best possible advice
directly from a Canadian immigration officer. I think this would be a better investment that spending, potentially, lots of money
on a lawyer who doesn't get the right result. It would only cost you $200 (Canadian) for the rehabilitation.