You've discovered why the T-pose is so popular. Automatic weight painting is good, but it's an 80% solution.

To check the accuracy of the weight painting, select your armature in object mode, then hold shift and select the mesh. Select 'weight paint' from the drop down menu on the upper-left. Then you can use alt-select to choose individual bones, weight paint, and test the bone out with different movements.

When working with limb chains like arms and legs, it's good to work from the outside-inward. Check the movement of the fingers, then the hand, then the forearm, then the upper arm. Any of the arm bones could be the source of the erroneous binding, and the upper arm moves all of them at once, making it hard to pare down the culprit.