Can I cross the land border from the USA into Mexico by car and return to the USA by car with an older version of my green card which has no expiration date?
Green cards issued between 1979 and August 1989 do not have expiration dates and do not need to be renewed unless you wish to use Global Entry kiosks at international airports in the U.S. you will have to get a replacement card. GE kiosks cannot read the old format Green cards.
If you have a Green card that was issued before 1989 and the photo was taken when you were a child, you may want to renew it even though its not required. If a CBP Officer is unable to identify you from the old photo as the legal owner of the green card, you could be delayed until your identity is verified.
To add to the other answer, if your green card is an I-551 with no expiration date (these were issued in the 1980s), it is still valid today and can be used for all purposes that the green card can be used for, including for work and re-entry to the US.
However, if your green card is an I-151 (these were issued before the 1980s), it is no longer valid now even if it had no expiration date. Although you are still legally a permanent resident (your status doesn't expire) despite not having a valid card, you might have some trouble re-entering the US, though they should still let you in eventually if it is obvious that you did not abandon residence. And in the worst case, if the immigration officer at entry doesn't let you in, and you refuse to voluntarily give up your permanent residency, then they would have to refer you to removal proceedings in immigration court, and I believe that the immigration judge will cancel the removal proceedings and let you in since it is clear that you did not abandon residence.