The triplex looked good. Decent location, solid building, new roof...but we offered 25% lower than the asking price, which was also very low to begin with. Why? Well, besides the deferred maintenance, fire code issues, smell, and layout (one of the shower stalls was in a bedroom closet!), the reason we needed a further discount was the tenants.
This place was obviously run by them. Don't let this happen to you! Not only will they give you a management headache, but when you sell, if you can at all, the buyers will want deep discounts.
You don't have to be a tyrant, but set rules and enforce them. They may not like you, but they will respect you. You probably didn't get into real estate investing to make new buddies!
Inherited tenants can be tricky. They are used to running the place, and you probably will have some issues. We find a businesslike, firm approach works well. Setting rules, and enforcing them may turn some of your inherited tenants into keepers!