I have owned a Mini 3 Pro since March.  Flown a good bit and never had this issue.  

Video was blurry and choppy today.  Re-calibrating IMU did not work.  Re-center gimbal did not work. Swapped out a questionable propellor (both ones) just to be safe.  No difference.   
Also noting that after I cut the drone off, I hear a motor around the gimbal run for like another 20 to 30 seconds.

I'm in touch with DJI but curious if others had this issue.  Thank you.

https://www.youtube.com/watch?v=TDzsgd4RU9c

Most probably a gimbal motor is the cause of this vibration.

My Mini 3 Pro was replaced very early on due to such a problem with the gimbal....

... just a few weeks after purchase.   

Unusual amount of jello related threads popping up on this forum lately.

Hi, RamblinMan. Thanks for reaching out, and we're sorry for the inconvenience. Were there strong winds when this occurred? And have you also checked whether there are foreign objects stuck on the gimbal? How about calibrating the gimbal? And since you mentioned you already contacted DJI, was the drone sent it already? Thank you.

DJI Tony Posted at 6-6 02:50
Hi, RamblinMan. Thanks for reaching out, and we're sorry for the inconvenience. Were there strong winds when this occurred? And have you also checked whether there are foreign objects stuck on the gimbal? How about calibrating the gimbal? And since you mentioned you already contacted DJI, was the drone sent it already? Thank you.

Hello.  No strong winds.  Almost no winds.  No foreign objects.  I did not see a calibrate gimbal option.  I saw "re-center" gimbal as I mentioned and I did that.  No change.  

I have the drone boxed up beside me with the DJI return label on it to drop off later today at UPS.

Someone posted a similar comment a few weeks back on another forum.
- Set the drone on a table and record some video.  Prop's not running.  Don't move the gimbal around.  Take a video.  See if it has the jello effect.  If it does.  It's most likely a sensor issue.
- Next, with the drone still on the table, prop's not running, move the gimbal around and record video.  See if that causes an issue.

- Next, lift the drone and "fly" it through the air using your hands - prop not running.  Take a video.  See if there is a jello effect.  Same deal.  Most likely a sensor issue.  Repeat. This time "flying" and moving the gimbal around.  See if that's the issue.

- Next, you guess it.  Hover the drone.  Take some video while it's just hovering.  If there is a jello effect, it's the props.  

The good news is that if you send it to DJI and they can't figure it out, they'll just send you a new drone.  That's been my experience anyway.

RamblinMan Posted at 6-6 06:55
Hello.  No strong winds.  Almost no winds.  No foreign objects.  I did not see a calibrate gimbal option.  I saw "re-center" gimbal as I mentioned and I did that.  No change.  

I have the drone boxed up beside me with the DJI return label on it to drop off later today at UPS.

We're sorry for the inconvenience. If the device is already on its way to the DJI facility, then we assure you it will be handled accordingly. You may contact Customer Support if you want to check the progress or want to know the result of the assessment. Thank you for your understanding.

As an update to my situation:

DJI received my drone and wrote me today with an update.  Apparently the Gimbal Pitch Axis arm was bad and so was the Gimbal Roll Motor Module.  They estimated an $88 repair bill which they are waiving as under warranty.  The letter said they would either repair or replace it with a product that's new or equivalent to new.  Guess I won't know until it arrives.

RamblinMan Posted at 6-9 22:03
As an update to my situation:

DJI received my drone and wrote me today with an update.  Apparently the Gimbal Pitch Axis arm was bad and so was the Gimbal Roll Motor Module.  They estimated an $88 repair bill which they are waiving as under warranty.  The letter said they would either repair or replace it with a product that's new or equivalent to new.  Guess I won't know until it arrives.

Sorry for the late response. We're glad that you previously received an update on your case as part of the process of our online repair. If you need help doing set up your new unit or encounter any issues, please don't hesitate to reach us. Thank you for your valued support.