Below is a summary of selected additional activities in Market District.
1) Mobile Command Centre - D.U.P. base is located near water in south-eastern part of district. It is not typical construction because enemy forces occupy two different levels - upper highway and lower yards and streets. Regardless of which level you want to clear first (even partially) you have to be aware of an elite soldier with powerful powers and minigun. As a reminder - keep attacking him until he creates a shield. After that quickly run towards him and finish him.
Another threat is Auto Turret. There are several of them placed on the lower level. Their fire is very painful for your character so make sure to avoid them at all costs. You can use distant attacks to destroy them or disable them when you get close to them from behind (screen above). Mobile command centre is located on the lower level (under the highway, next to a small parking lot). I suggest destroying it only after elimination of an elite soldier and auto turrets.
2) Blast Shards - One of shards is located over water (north-western part of district). Start on the nearby railing for example and alternately hover over water and use Smoke Dash. Try to land on wooden stakes.
3) Hidden Camera - The camera you're looking for is located in the place shown on the above screen.
4) Audio Log - You have to get to the narrow alley shown on the above screen. Hard disk can be found on the right.