A Health IT Application Store?

You don't need a 'platform'. An interoperability specification is the platform and it needs to be open to ensure wide adoption and innovation. EHRs now are closed systems with limited data import and export over largely proprietary and/or obscure protocols. This keeps the customer captive but stifles the kind of innovation you are trying to foster.
In order for this to work, you will need to have open interoperability specifications. You need to have a way that an eRx application can talk to the patient index to get patient demographic information and also talk to the EHR to get allergy and current drug information.
Each of these modules needs to be able to generate and respond to messages to send and receive the information it needs. This should all be done through open interoperability specifications.
If you do this, anyone can create a new application that can find the information it needs and adds value.
You can give grants and prizes but I think these should be given for the open interoperability specifications and implementations. Once these are in place, the new applications will arrive.