The stoush between SAP and Waste Management [1] as reported by PC World highlights the issues at the heart of vendor selection:

SAP used "fake" and "rigged" software demonstrations to convince Waste Management its products were a good fit, according to the trash hauler. But after years of work and great expense, the product did not work satisfactorily, Waste Management claims.

But SAP has denied any wrongdoing and counters that Waste Management breached its contracts with SAP by failing to "timely and accurately define its business requirements" and provide "sufficient, knowledgeable, decision-empowered users and managers" to work on the implementation.

First: identify your business requirements.  Setting out a checklist of essential functionality might sound like overkill, but incorporating the checklist and the vendor’s responses into the contract may help give clarity later.  Checklist availability can be found on our main [2] site and at [3] Public Sector Assets

Second: be in control of the selection process.  Define the script of what you want the vendor to demonstrate.  Home in on the key aspects.  Ask who else uses the software in that way