On the S3 I just type in about:debug in the address bar and it comes up but it doesn't work on the S4, it seems to do an autocomplete for chrome://debug.
Firstly it would be great to know how to get the console open and secondly why would Chrome's autocomplete be coming up for the stock browser?
I don't know how to activate this console.
But I have used a tool that can allow you to remote debug any browser with limited changes to your web page (only add one script). It is VorlonJS and you can find demo here: http://vorlonjs.com/#demo
try this link remote debugging chrome.
Well if are you developing on android greater than 4.0.3 you can type
adb logcat and you would be able to catch your console.log or errors.
Or if you want chrome enables mobile screen to test the view.It depends if you are testing the functionality or the graphics