When any field is invalid, if you try to get its value, it will be undefined.
Lets say you have a text input attached to $scope.mynum that is valid only when you type numbers, and you have typed ABC on it.
If you try to get the value of $scope.mynum, it would be undefined; it wouldn't return the ABC.
(Probably you know all this, but anyway)
So, I would use an array that have all the elements that need validation that I have added to the scope and use a filter (with underscore.js for example) to check which ones return as typeofundefined.
And those would be the fields causing the invalid state.