Note that the argument passed to $save
should be a string, pointing to the key name that you want to save.
Secondly, when you define new properties on the scope object, they'll need to be at the right path (you're missing the UID of the client when saving the team).
Thirdly, if any of the pieces of data resolves to undefined
the data will not be saved. Ensure that everything under the team is either a variable that has a value, or is a string.
var firebaseURL = 'https://<myfirebase>.firebaseio.com/clients';
$scope.clients = $firebase(firebaseURL);
...
$scope.clients[clientUid].team = {
"Bob": {email: "some address", position: "developer"}
};
$scope.client.$save(clientUid);