1. It was the private drive of Howard Stark- of course he's under camera surveillance, yes, even in 1991. Dude was the brains and founder of SHIELD. His entire property was probably under watch.
2. Perhaps the WS had already scoped out the location and knew the camera was there. It may have even been included in the mission they gave him. Killing Stark and his wife on tape perhaps may have been some sort of insurance for Hydra, which is why he shot out the camera after it was done, not before.
3. Remember that Hydra was embedded in SHIELD, so the surveillance may have been put there by SHIELD but a mole from Hydra could have retrieved the tape to hide what had been done.