How to do forensic check in property transactions?

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Hi Guys,
I have paid a nominal token advance and my lawyer hasn't found any issue in the papers. The EC also looks fine. I am aware that the bank's legal team will also check the papers. ( This is in old Bangalore/CBD limits and it has an old demolish-able house. So there should not be any concern on the title of the property). But I am apprehensive about other aspects like seller's profile/intent etc. ( I dont doubt him. But you never know in these property transactions. Also, the lawyers wont be able to check everything.)
So my question is, do people do forensic check/background check before buying the property?. If yes, how do we go about it?. What are the things to look for?. Some of the common issues I come across in net are forgery in the original documents/signatures, pledging, multiple wives ( may not be an issue in this instance, since the property is in the name of seller's wife and its not inherited). Should we also check if there are any criminal cases?. Also, if the sellers gets to know that we are doing these investigations, he may get offended and call the deal off.
Thanks in advance.