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

Then, you fail to check his criminal history, and he then wrecks your neighbor's windows in the property next door to the tenant.  

I am assuming you have done criminal background checks as well?  

. #1 it's illegal, if the tenant can prove what you did, you'll get sued at best, or maybe arrested for theft or criminal mischief.

Check out Northwest Justice Project : Your Rights as a Tenant in Washington State.

I discriminate all the time against people who don't have good credit or who are criminals, etc."  

Some states limit you on how much you can charge the tenant, some let you charge whatever you want.I never used Smartmove, so I don't know if they have an option where they will also do criminal/eviction/employment/landlord, etc. on top of credit.We used these guys:http://www.cbacredit.com/Index.aspxWe didn't pay for their full service option, as I did some of the tenant screening myself, but they do offer full screening, including employment, landlord references, etc.In CA, for example, you can only charge around $42 for the application fee, even if it costs you more than that.  

Unlike tenant eviction which is handled at the District Justice level and is easy to do yourself without an attorney, Ejectments must be done in the Court of Common Pleas, and while you CAN do it yourself, in almost all cases you will need an attorney.If they are the former owners or a tenant with a lease, then they are not trespassers, and their removal is not a criminal matter but a civil matter that will not be helped by you calling the police or filing a police report. 

She had a good job, good references, good credit and nothing criminal that I could find.

While, I recognize that breaking and entering is criminal conduct, I also recognize that it is possible to possess abandoned property without violating the law.You are correct that in many States forcible entry is indeed defined to include more than physical breaking.