I don't agree with Phx that you have any issue with Mexicana, even if everything that went wrong was their fault.
This is classic pisspoor customer service, in which each airline blames the other. Your contract was with Continental to get you to Cancun. If they chose to route you via one of their partners, that is their business. You had to buy more tickets to get you to Cancun, and Continental should be on the hook for that. If Continental have an issue with Mexicana and how they dealt with it, let them take it up with Mexicana. I would write out a comprehensive, detailed timeline of everything that happened and provide a copy of the receipt for your tickets. Send it to Continental, signature on receipt, then copy the letter to the DOT.
I would not pursue the lost night at the hotel. Continental have a legitimate defence that there were extraordinary circumstances beyond their control. However, there is no defence to their failure to get you to your ultimate destination without you having to shell out.
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