**Core Concept**
Traumatic anterior dislocation of the shoulder can lead to injury of the axillary nerve, which is a branch of the posterior cord of the brachial plexus. The axillary nerve provides motor innervation to the deltoid muscle and the teres minor muscle, and sensory innervation to the skin over the lateral aspect of the shoulder and the upper arm.

**Why the Correct Answer is Right**
The axillary nerve is at risk of injury during traumatic anterior dislocation of the shoulder, particularly when the dislocation is forced or when there is a significant degree of displacement. The nerve can be stretched or torn, leading to weakness of the deltoid and teres minor muscles, and sensory loss over the lateral aspect of the forearm. The symptoms described in the question, including sensory loss in the lateral side of the forearm and weakness of flexion of the elbow joint, are consistent with an injury to the axillary nerve.

**Why Each Wrong Option is Incorrect**
**Option A:**
The radial nerve is a branch of the posterior cord of the brachial plexus, but it is not typically injured in traumatic anterior dislocation of the shoulder. The radial nerve provides motor innervation to the extensor muscles of the wrist and fingers, and sensory innervation to the back of the hand and fingers.

**Option B:**
The musculocutaneous nerve is a branch of the lateral cord of the brachial plexus, and it provides motor innervation to the biceps brachii, brachialis, and coracobrachialis muscles. While the musculocutaneous nerve can be injured in shoulder trauma, the symptoms described in the question do not match the typical presentation of a musculocutaneous nerve injury.

**Option C:**
The ulnar nerve is a branch of the medial cord of the brachial plexus, and it provides motor innervation to the flexor muscles of the forearm and hand, as well as sensory innervation to the little finger and half of the ring finger. The ulnar nerve is not typically injured in traumatic anterior dislocation of the shoulder.

**Option D:**
The median nerve is a branch of the lateral and medial cords of the brachial plexus, and it provides motor innervation to the flexor muscles of the forearm and hand, as well as sensory innervation to the palmar surface of the thumb, index, middle finger, and half of the ring finger. The median nerve is not typically injured in traumatic anterior dislocation of the shoulder.

**Clinical Pearl / High-Yield Fact**
The axillary nerve is particularly vulnerable to injury during shoulder trauma because it is stretched or torn when the shoulder is dislocated or fractured. This can lead to weakness of the deltoid and teres minor muscles, and sensory loss over the lateral aspect of the forearm.

**Correct Answer: A. Axillary nerve.**