@Krista Olen- I actually have an iguana. He requires a massive cage. I had this professionally constructed and looks appealing and is in a separate room. I would NEVER allow a tenant to have one, especially in my smaller units. He can absolutely leave a very disgusting mess if I don't clean up after him, feces and skin he sheds. He requires a rather complex lighting system, that I could see being a fire hazard with less than careful tenants. I'm sure he could cause some damages, mainly from knocking stuff over/climbing on stuff. I got the appeal, but a lot of people are terrible at taking care of reptiles.
You should require them to show you the cage they will be using to make sure it isn't unsightly(future showings). Ensure they know how to properly set up the heating lights to avoid fire hazards. Ideally limit small reptiles that can fit inside a 50 gallon tank , stick to herbivores. I also had a bearded dragon when I was a kid. I was careless and allowed worms to get out....they turned into beetles. My parents were not pleased and I'm sure you as a landlord would be even more so.
Never underestimate the power of people to royally screw up with even the most simple of pets.