All airline, charter and private aircraft flying to and from Mexico file an electronic APIS prior to flight. So far, we are not aware of the Mexican authorities sanctioning any private flight for failing to submit an APIS.
Just a few years ago the only option available for filing a Mexican APIS is through a “for profit” portal, unlike the public portals available for submission in other countries (USA and CARICOM countries). But lately, AOPA mentions there is a simple form of APIS that can be filed. We invite to take a look at it here. 
If you are planning to fly in the Caribbean area, including Cuba, Pilot Publishing has a
highly recommended book on the subject called the Bahamas and Caribbean Pilots Guide, available at www.pilotpub.com.
The government of Mexico no longer requires that you purchase liability insurance that is underwritten by a Mexican company – call your current insurance company to get a Certificate of Insurance compliant to Mexico’s requirements, go to this link to download and print this letter with Mexican requirements, both in Spanish and English from the Director-General for Transport and Air Control, Mexico. (As a precaution, carry this letter as well as your Mexican compliant Certificate of Insurance with your aircraft documentation while flying in Mexico).
The COPA Group Aviation Insurance policies (VIP Gold, VIP Silver and/or VIP Bronze) cover Mexico. Our policies act as excess of any liability insurance purchased from an insurer licensed under the laws of Mexico. It is worthwhile noting that your COPA VIP Insurance Policy will still act as the primary insurer in case of a claim.
However if your current insurance policy does not cover Mexico, the Mexican government requires you to purchase extra coverage.
COPA recommends MacAfee and Edwards for anyone requiring additional coverage underwritten by a Mexican company:
MACAFEE & EDWARDS, INC.
260 S. LOS ROBLES AVE.
SUITE 303
PASADENA (CA) 91101 1-800-334-7950
For information on flying in Mexico, contact the Baja Bush Pilots Association.