UPDATE
Angular offers now the two scope methods $watchGroup (since 1.3) and $watchCollection. Those have been mentioned by @blazemonger and @kargold.
This should work independent of the types and values:
$scope.$watch('[age,name]', function () { ... }, true);
You have to set the third parameter to true in this case.
The string concatenation 'age + name' will fail in a case like this:
Before the user clicks the button the watched value would be 42foo (42 + foo) and after the click 42foo (4 + 2foo). So the watch function would not be called. So better use an array expression if you cannot ensure, that such a case will not appear.
http://plnkr.co/edit/2DwCOftQTltWFbEDiDlA?p=preview
PS:
As stated by @reblace in a comment, it is of course possible to access the values:
$scope.$watch('[age,name]', function (newValue, oldValue) {
var newAge = newValue[0];
var newName = newValue[1];
var oldAge = oldValue[0];
var oldName = oldValue[1];
}, true);