I am developing an Application using Xamarin (For iOS and Android) and faced an issue, When the application is installed (Android) in Debug mode it will work fine, but when I create APK or install directly using Release mode it will show error. The error was related to Sqlite operations. I am able to solve the issue, so thought it will be helpful to share the solution which worked for me. This Solution may work for other who also have similar issues with some other third party dlls.
Right click on Android project, Go to Properties the to Android Options and make sure you are using release mode and check Linking
There are 3 Linking options
SDK Assemblies only
SDK and User Assemblies
These three will have difference in what the Xamarin compiler will add in your APK, if you use None the size of the APK will be large and also the application will take more time to load.
Solution: All you need to do is change the Linking options and try to build it. Always Clean and rebuild the solution before testing. This how I fixed Xamarin APP working on debug mode not on release mode issue for me.
For me I was using SDK and User Assemblies and changed to SDK Assemblies only, and it worked.