What is the commonest neurological complication of HIV?

Peripheral neuropathy.

Specifically, the neuropathy tends to be painful, and is most commonly felt distally, usually in the legs. It is a polyneuropathy, inclining to be bilateral and symmetrical.

The pathology is well characterised, and includes distal degeneration of the long axons and prominent local macrophage activation. Just why these things occur is still a matter of debate, however. Options include immune dysregulation, a leaky blood-nerve barrier, neurotoxic byproducts of HIV replication, treatment toxicitities and even opportunistic infections.

Is there anything you can do to treat it? Yes, although the results vary.

The most obvious starting point would be analgesics, but not all of them have been shown to work better than placebos. The most well-established analgesics are the opioids, used both systemically or locally, but they have their own associated problems (like addiction). Other options are lamotrigine (an anticonvulsant), lidocaine cream (a local anaesthetic) and local capsaicin patches. A summary of a recent study with high-dose capsaicin patches can be found here.