I assume no felonies, no sex offenders, no evictions.  

Lived in Melbourne, Sydney AU and Auckland NZ myself!

It's a high crime area, and there's a registered sex offender, literally, living right next door.

An older HUD memorandum says we can deny housing if someone is on the Sex Offender Registry.

As a landlord you are able to obtain credit reports, nationwide criminal, nationwide eviction, along with a bunch of other reports (sex offender, county level criminal, etc).  

In the event an applicant is rejected and reports me for an FHA violation I can prove I didn't even know the person was a convict, etc.If an applicant makes it this far and then a background check turns over a criminal history I will have to manually see if this history conflicts with having a legitimate and substantial effect on the community (e.g. a sex offender in an MHP full of families with little children is a non-starter for me).

@Sarah SimpsonRTA is similar in most crown countries: CA, NZ, AU, UK, etc.I lived in Auckland NZ and renovated 5 properties and "lease 2 owned" 1 rental.RTA Residential  Tenancies Acts are all similar. :)

Their floor squeaks badly when they have sex and to top it off my bed shakes with their movement.

The federal Fair Housing Act of 1968 and the federal Fair Housing Act Amendments Act of 1988 prohibit discrimination on the basis of the following criteria (called “protected categories”): race or color; religion; national origin; familial status or age—includes families with children under the age of 18 and pregnant women; disability or handicap, or sex.

In one case, the Seller arranged for a six month free lot rent for his son only later did the new Owner find out the son was also a registered sex offender!