I am having the same problem on my Samsung Galaxy s4, but it is not only when recording video, it also happens when recording just audio.
I know that the static is in the actual recording, because the static is in the same place every time during playback, and I can open the audio file in an audio editor and see the static in the wave form.
My Samsung galaxy s4 is only about 3 months old has been always treated very carefully -- never dropped or left in extreme hot or cold or had any extreme flexing or bending applied. It has almost always been in a protective case.
As other users have stated, this static occurs randomly regardless of environment, whether its loud or quiet. I have ensured that no other electronic devices or fluorescent lights are nearby which could be causing interference.
The phone is not plugged in to and a charger but is running off a fully charged battery, so it's not line noise.
I will probably end up calling Samsung about this if I can't find a solution like a software or firmware upgrade. I have seen on other audio devices where static can be caused by flow level computer code which is flawed or executes too slowly sometimes, so it is not out of the question that this can be fixed by software or firmware. I should check for both, but there will be a learning curve to figure out how to do that, and I'm short of time. I'm dictating this with Google Voice as it is.
I hope someone can help us resolve this issue. If I can magically find time to be more proactive and contact Verizon and have any luck getting it resolved, I will post my results back here. But it's doubtful I will find time, so I'm hoping someone else might post a resolution....
Many thanks in advance to anyone else who might have time to track this down and share findings here,
- Bob