One of my tenants in a 4plex bought an inflatable pool and told them politely that I don’t allow those things due to electrical hazard precaution.

Even as a precaution, the thermostats for the heat are programmed not to exceed certain temperatures, so that is controlled to an extent as well.  

Be sure to take precautions not to get paint on hardware and fixtures.Is she a responsible pet owner?

I would be upfront with them what happens if one moves out but as a precaution make sure both are on lease but look at the less qualified of the two applicants and see if they still meet your criteria for renting individually.

I guess at the end of the day I have the best sense of what requirements I can get away with in my market and I'll have to decide the right balance between screening precautions and filling the unit.  

People who take precautions are not fooling themselves.

The problem is whether I would get in trouble for doing it, and if there were any legal ways to do it or precautions I could take to not get caught.

Any extra precautions that landlords should heed in addition to the standard tenant screening?

What extra precautions should be taken before hand?

We have accounts specifically for tenants to deposit into, and we transfer balances out every few days to accounts that the tenants don't have the number to, for a safety precaution.