Some things that the desert could use:
More unique item drops, especially in hardmode. Other than the sun and moon masks, the hardmode underground desert enemies don't drop anything that you couldn't get on the surface. A Desert Mimic with unique drops and a Desert Biome chest in the dungeon would also be cool.
More unique loot from chests. Maybe some of the pyramid loot could get moved to sandstone chests in the desert, plus some cool new loot, as well.
More uses for antlion mandibles (and light and dark shards too).
A revamped pyramid with some of the 1.3.1 traps/mechanisms added, plus a few new ones. Perhaps give it some new loot, as well (or a boss that you can fight).
An Oasis mini-biome that can spawn on the surface or underground. This would add lakes with some palm trees to the desert, to add some variety. The Oasis would also come with new unique fish to catch, and quest fish for the angler (plus the ability to get desert crates). However, it might also be home to dangerous enemies such as crocodiles, so you can't get too comfortable(though maybe you don't start getting crocs in the oasis until hardmode, so they're relatively safe until then).
A Snake Pit mini-biome, which is similar to the spider nests, except with deadly snakes and snake-themed drops/equipment.
The ability to craft sandstone blocks into sandstone bricks. Sandstone furniture would also be cool for desert builds. Maybe also the ability to craft silk and wood into Silk Blocks and Silk Block Walls to create tent-like buildings for the desert.
In short, it'd be nice if the desert got as much content as the jungle, or even the snow biome. (The snow biome could use some more content, but that could be saved for another update since the desert desperately needs the attention more)