When the kids had health problems (my brother broke his arm, my sister had a severe allergic reaction), he failed to pay the ensuing medical bills. 

So you can say "my kitchen must be kept kosher" and put some rules in place for that, but you cannot state "I only accept Jewish roommates".If you are allergic to pets, you may opt not to accept a roommate that requires a service dog or emotional support animal. 

If your allergic to dealing with a few delays or inconveniences I’d say go for post 1990’s construction where the slabs tend to have less foundation issues, for example.

That sounds pretty daunting, but luckily most issues (other than a very high water table) are solved with very little money unless you're allergic to a shovel and a few hours of manual labor.1.

Allowing a dog in a shared living space with another tenant being allergic is probably not reasonable.

Cats are another story however and I'll first admit I am biased because I am very allergic. 

I'm allergic, so he's never coming in, but I was fine with a "barn cat" model, keeping pests away.

"I'm allergic to the water."

And anyone who lends you the cash for downpayment will also be allergic to 2nd position.

You may have someone that is allergic or irritated by smoke, so it's always worth disclosing up front.