Running a credit and criminal check without a SS# is a waste of time. 

I was wondering, can you put a clause in your lease that says if the landlord even suspects criminal activity with or without proof, the tenant could be found in breach of the lease and evicted.

How do you know these extra people aren't criminals?

Many posts assume the tenants are criminals.

Also someone who tries to "talk" you into accepting them with visions of "hey, I've got the security deposit and first months rent right here" so you can skip the credit/criminal/income/previous rental history (that's often the last rent you'll ever see from them) .  

Unfortunately it's much more difficult to obtain credit and criminal backgrounds on Canadians and other foreigners.  

Potential Tenant has clean criminal background, credit not so great (560)Recently divorced, single mother of 4. 

I just received my first applications back along with their credit/criminal history.

One is a criminal action, the other civil.  

You can also limit based on credit score and criminal activity if you have a consistent written set of criteria.