appView.addJavascriptInterface() does not work on API 17

From the Android 4.2 documentation:

Caution: If you've set your targetSdkVersion to 17 or higher, you must add the @JavascriptInterface annotation to any method that you want available your web page code (the method must also be public). If you do not provide the annotation, then the method will not accessible by your web page when running on Android 4.2 or higher.

Source: Android WebView Doc (emphasis added)

What you have to do on API 17 is annotate your method with @JavascriptInterface:

public class CustomNativeAccess {
   @JavascriptInterface

and then get rid of the constructor part:

/*private WebView mAppView;
    private DroidGap mGap;
    public CustomNativeAccess(DroidGap gap, WebView view) {
        mAppView = view;
        mGap = gap;
    }
*/

Also be sure you import JavascriptInterface in your project:

 import android.webkit.JavascriptInterface;

You can read about it more here: WebView Android

Edit: You will have to annotate each method with @JavascriptInterface within your class that you'd like to access from Javascript.