Google should provide an application security check
Why doesn't Google offer an application security check as an optional thing for application developers to put their apps through. Clearing the check could give applications a "Google Approved" badge which gives strong reassurance to users that the application is safe. Being optional means that developers don't need to put their applications through that but without having the badge would mean that users would possibly receive a warning that it is an unapproved application (similar to Microsoft signed drivers). Integrating an application filter whether the user wants to see only approved applications or all applications could also be added. This scheme would give the best of both worlds (Apple's application security checking and Android's openness).