Maybe the way they manage, how long they've owned it, pet policies, who pays what utilities, etc.  

People sign leases stating that they agree to no pet policies all the time, yet, they still bring them in.

Think of all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.

There is a lease in place, with a security and pet deposit that was transferred to us at closing from previous owners.Do we need to sign a new lease, or would the one that tenant signed with the previous owners suffice?

I'll usually find other incentives such as waiving a pet fee (if applicable), waiving an application fee if I am relatively certain they will be a good applicant, I also make some concessions with water payments (can explain in greater detail if you'd like).  

I am not keen on returning any of this money back to the main tenant as it is very evident that the damage he has caused on the property with a rotating cast of characters and a pet is likely significantly higher than $2000.5) Legal fees and other costs: Can we include a demand for unpaid rent, legal fees, and other costs in the eviction process for our tenant or does this have to be a different suit?

reading books and networking also helped.I learned many of the tricks and creative stuff they were teachingSome of the courses were great, others just sucked the green out of my jeans.I started attending public auction - buying war zone houses - using credit cards and credit lines - borrowed money and the really biggie creative financingThe most important thing I learned about about creative financing is that I DID NOT need to suck up to lenders - yippeeI than discovered a cross pollination of the concepts of creative financing - the synergism of ideas helped me develop new creative financing techniques.Some of those formulas I still use today to close transactionsI work a formula known as Control and Roll - this is a system of controlling real estate with little or no money and assigning the contract within 3 weeks for cash using the auction method of marketing - this system circumvents all of those who want to slow an investors down - like banks - underwriters - inspections - condition of property - agents and others.During those struggling days - I also used a system called "Check Funds" this allowed me to control many buildings without the need for down payment money.Hybrid offers is another one of my pet formulas - this is where the seller becomes a partnerDelayed settlement techniques - with soft contingencies - getting automatic extensions without the need of being rejected.

Most LLs charge extra for pets.

There seems to be a shortage of rentals for families with pets in that area, and I have received two offers to rent should I decide to go forward with this deal.

I didn't plan on allowing pets without a separate deposit.