What is Causing this discoloration?

[Briscactus]

The edges of the plant's largest bulbs have been browning for several months but recently it's started to get worse. Can anyone identify what is going on and what I might need to do?

[toadstar]

It looks a bit like sunburn. What is your location and the conditions that you're growing it in?
http://cactiguide.com/article/?article=article4.php

[Briscactus]

Brisbane, Australia. Decent sun but the yard has several trees that keep it from being totally blasted.

[greenknight]

Agreed, that looks like sunburn. Find a shadier location for this one.

[Brontosaurus]

On the parts where the brown outer layer is clearly dead and would come off with a little pressure (like the brown spot next to the areole right in the middle of the photo), is it better for the cactus to remove the dead flesh or leave it on?

[hegar]

If the dead areas around the areoles are only present on one side of your plant and the damage is mostly present on the new growth of the top, most likely it would be sunburn damage. Was the plant recently moved from one location to another or did you change the vegetation around it, if the cactus is growing outdoors? Things like that can also make your plant more susceptible to sun damage.
Otherwise, I would check on the plant regularly, in order to see, if the dead areas are becoming larger or any abnormal softness develops. Those changes may indicate the presence of a pathogen or onset of a rot.

Harald