Not limited to Mexico but certainly relevant. You need be very sure what is included and what isn't. Not sure where you are looking but keys are whom pays electricity and water. LP gas normally not included nor are phone calls or internet. If renting furnished, what is your liability. Is there a maid/cook or gardener that you are responsible for. Is the lease fixed price for what period. Is a deposit required.
Depends where you are looking (I see your in Mexico City).
Specifically, see what the maintenance fees are and if they are included in the rent or not, some places can charge 200 to 300 USD in some more expensive places.
See if telephone lines are hooked up or not (some apartments never were and a lot of people are cell only and couldn't care less about the net).
If you're a foreigner see if the landlord is the type that wants as 12 month firm rental (meaning you leave early, you pay the remaining months) or can work out what I like to call a diplomatic clause, often it's a forfeiture of deposit (if nothing wrong) or one month's rent if you have to go. My cousin did something like that when he lived here, because he never knew if his company would transfer him back to the U.S. or not.