A mutation would die out unless it was useful, and these forelegs are so common among T. Rex's ancestors, (including Allosaurus who lived tens of millions of years earlier), that it suggests they played a very useful function.

The same argument could be used to rule out the vesitigial structure theory. T.Rex was one of the last of the dinosaurs to go extinct, it's forelegs were just as developed as it's ancestors' were, there is no sign of a "vanishing organ" over time.

The feeding accessory organ theory mentioned by Nick makes sense, but it's hard to reconcile with the fact that the limbs could not reach the mouth.

Manipulation of young or nesting materials occurred to me, too, but it's hard to visualize just how it would work. If it reached down to pick up an egg or a pup, it wouldn't be able to see what it was grabbing because those tiny claws are so close to its neck. Imagine a chicken picking stuff up off the ground with little hands growing out of it's breast. It doesn't add up.

"Useless" organs, like peacock tails or bird of paradise plumage, are often associated with sexual selection and courting behavior, but they also are possessed mostly by the expendable males. The females are usually plain and unencumbered by these decorations.

Perhaps they were some sort of grooming accessory. If the big carnivores were carrion eaters, the minilimbs may have been used to keep the neck area clean or free of parasites, but I'm just speculating here.

None of these suggestions can be totally ruled out, of course, but neither do any of them sound very plausible.