@Michael Lee,
Don't fall for this "I'll pay six months rent/deposit/whatever in advance if you rent TO ME." This is a red flag. Follow your written rental criteria that has been approved by a fair housing attorney when screening tenants and you will sidestep these potential tenancy nightmares. BTW - loved your response to the lady who threatened you with her attorney!
Here's a few other red flags to look out for:
"I have to move in today." - Always ask for this. There may be exceptions but usually this means they have no rental history or they don't want you to know their rental history (landlord wants them OUT!)
"I want to pay the first month's rent and deposit now, with the application, to be sure I don't lose the rental to someone else." - You still have to screen the person. You don't want them accusing you of taking their money when they didn't qualify.
"I already have a copy of my credit report so you don't have to pay for one." - These can be bought online. You can respond to the tenant that "You'll be paying for it."
The applicant gives you a check for the screening fee and the address on the check doesn't match current check on the application. - First only accept guaranteed funds (money order, cashier's check) for first month's rent and security deposit. Address on driver's license should also be current
The applicant's consumer credit report shows addresses applicant did not list on application - This could mean they were asked to leave by these landlords (voluntarily or by forced eviction)
"I've just gone through a difficult break-up and you are going to find a few problems on my credit report. I really want this place and I would be willing to pay the rent for the first six months in advance." - see beginning of post.
The applicant appears to have lots of cash, but lists no means of support or source of funds on the application. - The last thing you need is a drug dealer or escort service renting your property.
The applicant does not want to furnish owner with social security number. This is not a red flag if the applicant is okay with you using his tax identification number.
The applicant can't remember names and phone numbers of previous owners - this is somebody else's problem. You are not the applicant's secretary or private detective!
The applicant has copies of his pay stubs with him, BUT there are no withholding taxes taken out and it's a W-2 type job - pay stubs can be purchased on line too with a courtesy call from their "employer."
I know this is a long answer, but I become upset when these professional tenants on wheels take advantage of hardworking people who just want to run a rental business and create a solid financial future for their family.
I hope this helps and good luck finding a tenant!