I agree with Stuart 100%, about having all your original paperwork, but Kelney's right. A baseball card would probably work just fine. It seems that I only get stopped and asked for paperwork at the border one out of every eight or ten times I cross. For stops on the road, I carry all the pertinant information readily at hand. I usually try to be friendly and polite, while handing them the papers one at a time as fast as they'll take them... one at a time explaining everything in English as fast as you can. The more paperwork, the better. :?
I lived in Mexico, and traveled all over the country. The Federales De Camino are pretty squared away, and won't bother you unless there's something obviously wrong, or they think you may need assistance. The soldados do it because that's their job. The transitos, or city police are entirely different. Gringos are a source of income. I've had transitos in several cities ask me for my papers and even Visa. Whether it's legal or not, they do it, so you'd best be prepared. I've paid la mordida a couple of times when I was in a hurry, but that's entirely your option.