Thanks for everyone's replies so far.
Nationality is Canadian. I'd be checking one bag. The flights through Mexico involve an overnight stopover - so that's what worries me in terms of safety. I'd have to find a hotel for the night, near the airport, and find a safe legit taxi to take to the hotel.
As another poster notes there is an on-airport hotel, but if it is sold out, you should book a hotel that provides pre-arranged transportation, where the driver is easily identified as associated with the hotel and/or has a sign with your name, and greets you in the terminal (preferably) or just outside (if so, make sure you have the cell phone number of the driver). Generally, this is a must any time you visit a country for a first time, especially a third world country, where you don't know the ins and outs of how the place works. With such arrangements, you will be very safe, and you won't have to suffer the indignities of the Department of the Fatherland Security.