Wrist drop results from radial nerve injury/palsy. The radial nerve winds around the shaft of the humerus in the spiral (radial) groove, making it highly vulnerable to injury at that site. The commonest cause is a fracture of the shaft of the humerus, which damages the radial nerve as it courses in close contact with the bone, causing paralysis of the wrist and finger extensors and the characteristic wrist drop.

Why not the others:

In Volkmann's ischemic contracture (a sequela of compartment syndrome, typically following a supracondylar fracture of the humerus or forearm fractures), pain is the most important and earliest warning sign - specifically:

This is the basis of the classic teaching: "pain out of proportion to injury, and pain on passive stretch" should raise immediate suspicion of compartment syndrome/impending Volkmann's contracture, prompting urgent decompression (fasciotomy) before the other signs develop.

The other options come later and are less reliable/more ominous but not the earliest warning:

This is why clinical teaching emphasizes: do not wait for pallor, pulselessness, or paralysis - pain (especially on passive stretch) is the key early warning sign that should trigger urgent action to prevent Volkmann's ischemic contracture.

Painful arc syndrome (pain on abduction between roughly 60-120 degrees, subacromial impingement arc) results from impingement of structures in the subacromial space against the acromion during that range - this includes chronic supraspinatus tendinitis, subacromial bursitis, and fracture of the greater tubercle (which alters the smooth gliding mechanism), so all three are recognized causes.

Charcot's joint (neuropathic arthropathy) results from loss of proprioceptive and pain sensation (e.g., in diabetes, tabes dorsalis, syringomyelia). Repeated unperceived trauma causes progressive joint destruction, effusion, and gross instability/hypermobility - classically painless despite severe deformity, which is what makes it clinically distinctive from other destructive arthropathies.

Gout is caused by deposition of monosodium urate monohydrate crystals, which are needle-shaped and negatively birefringent under polarized light. (This contrasts with pseudogout, caused by calcium pyrophosphate dihydrate crystals, which are positively birefringent.)

In post-polio residual paralysis, unbalanced muscle paralysis around the hip (with relative sparing/contracture of the tensor fasciae latae and iliotibial band, combined with hip flexor overactivity/contracture relative to weak extensors and adductors) commonly produces a flexion-abduction deformity of the hip, often with external rotation as well.

McMurray's test (flexing the knee fully, then rotating and extending while palpating the joint line for a click/pain) is classically used to detect meniscal tears. It is most frequently positive for tears of the medial meniscus (semilunar cartilage), since medial meniscal tears are considerably more common than lateral meniscal tears due to the medial meniscus's lesser mobility and firmer attachment to the joint capsule and MCL.