Most people read the front page of a service contract and stop. The boxes that matter are often the ones filled in quickly while you watch the screen, and a blank or wrong entry can stay that way for the whole term.
Match the car to the paper
Before you sign, compare the identification number printed on the contract with the one on the vehicle registration and the one on the car itself. Check that the odometer reading written on the form matches the dashboard at the moment of sale. If either is off, the claims department may treat the contract as covering a different car, and you will be the one arguing about it.
Check the blanks and the boxes
Look for empty lines, boxes that say see attached with no attachment, and terms written in one unit when the salesperson talked in another. A contract term written in years, miles, or both should match what you were told. Initials next to a corrected entry matter. A pen mark nobody initialed is a change you cannot easily prove.
Get a finished copy before you leave
Ask for a complete, signed copy in hand, not a promise to mail or email one later. If the seller says the paperwork will be finished back at the office, do not sign the unfinished version. Keep the copy with your vehicle records, not in a folder you will not open for years.
A sample contract gives you wording to compare against the one you were handed. Companies that post one are listed on this site's sample contract page.