If the mission starts and after the cutscene you don't have an objective, you more than likely have a camera in your weapon wheel.

You'll have to fail the mission, cancel the checkpoint and swap the camera for an alternative or just use the camera ammo.

The beginning of the mission sends you on a fetch-quest for a camera, so if you have a camera already, the mission will bug out.

Hopefully this fixes the issue, should you encounter it!