Residency requirements for permanent residents?

No restrictions as far as I know.    You do have to check in/out w/immigration when flying

Agree.

You have to check in and out with Mexican immigration if traveling by land or water too.

The fact is everyone including Mexican citizens are required to do so.  By land, car or bus, they don't bother to check visa stamps for Mexican citizens.  Once in Nuevo Laredo and once in Reynosa, a customs official directed me to the immigration office.  This was when returning to Mexico.  I hadn't checked out because the bus driver wouldn't stop.  I started off towards Micracion and when no one was looking, turned around and got back on the bus.

Since that time, I take a taxi from the Reynosa bus station on the way out, go through Migracion and take a taxi back to the bus station to continue to McAllen.  Taxi fare round trip is 80 pesos.

If you fail to check in and out and get caught, they say there will be a fine but couldn't tell me how much.  One day, I'll stop at the local office and ask again.

my husband has permanent residence in Mexico and migration office told him that he can enter and leave the country as many times as he like for an indefinite period.