I need to inspect javascript execution (webview widget) in an android application, while debugging; through SDK & usb cable and/or http/websockets; from destop compute
For android >= 4.4 (kitkat)
See Remote debugging on Android with Chrome
For android < 4.4 (Lower versions)
Use very good open source tool: weinre. See this video for help to use it. If you are familiar with grunt then you can use grunt-weinre
For quick view:
NOTE: if you want to debug webview/browser in your mobile device then you need to replace localhost with your machine's IP running weinre. And yes, all the devices should be on the same network.