The Notary Public and/or your lawyer will do a series of checks on the property and ensure that the property has a 'clean' history, and that there are no liens on the land (e.g. an old unpaid mortgage). Under Mexican Law, liens are passed on with title of the land - BEWARE!
Your Notary Public should also check that all land taxes have been paid during the last five years (if applicable) and that utilities (electric, gas, water and phone) have also been paid during the last two years. By Law, you are not liable to debts after these times.
Other items to be checked include: Checking all buildings are on tax registers and have the required building permits, utilities were legally installed and payments are up-to-date, the property is not jointly owned, or if it is, that both (or all) owners agree to the sale, and that the seller/s has/have the right to sell.
The Notary Public is legally responsible to ensure that all documents are in order and that all legal procedures have been adhered to. He will do a thorough check and will not destroy his reputation by hiding any problems, or potential problems from you.