This is pretty poor but let’s face it, no surprise at this point.
I know many who are not experiencing all these issues and I’m pleased for them.
For those who are, the real surprise would be a patch which actually makes usability better in general not worse or the same…
Don’t hold you breath IMO. There is a pattern emerging.
All jokes aside… it’s quit sad actually
But hey… at least we can bob around our boats in new scenery… yeah…
There are so many things that could be causing this lack of pitch stability.
It may help if you elimiate the one’s you can, for testing.
ie No winds
No AP
No movement of the Yoke once trimmed for level flight
then no movement of trim.
I find that any oscillation, will eventually diminish, but it only takes a small disturbance, to start it up again.
If that disturbance top too great, then the oscillations grow, instead of reducing.
Since this seems to be reported in all planes, (even addon planes), it may well be the in the general flight modeling ??
Complex, not easy to identify, so I doubt if there is going to be a fast and easy FIX.
Maybe just a Fudge & cover up – which will be a shame.
GOOD Luck ASOBO … hope you get to this sooner than later.
Sad thing is, they actually fixed it in the version before this.
Also, only happens as stated before when AP is active. Even the heaviest bobbing goes away immediately when deactivating AP.
I have been trying to highlight this since the 1st Patch.
Now, I have given up – I can’t even know or tell if ASOBO are even aware of the issue, let alone in a position to fix it.
At the moment, for me, MSFS is a great Visual Sim, and a useful tool to familiarize one with the scenery to expect on a RL GA VFR flight – well worth $60, just for that
I can cope with the Neo (my favourite plane) having a mild swaying. But the oscillation above is ridiculous. Agree that eliminating possible causes is sensible idea, but frankly this looks like an issue for Asobo. Reminds me of aircraft behaviour in FSX when you speed up the simulation x16 fast
Now that you’re saying this, that is exactly it. Like I’m speeding and up the sim to maximum.
Right - ASOBO will need to fix it, not the users, or the addon developers.
Just don;t hold you breath – they must be totally overwhealmed with so many other issues.
(Would love to be a fly on the wall, in some of their current Project meeting !!)
Just what I have been saying since the beginning. They need to improve their comms and feedback responsiveness. Compared the the cost of developing the sim, it would be a negligible expense and the infrastructure already exists.
I have the same problem with the bouncing Longitude. It’s so sad cause it is my favourite plane in the sim. 
The error can be found in the patch notes under Known Problems.
Longitudinal Static Stability - otherwise known as “dolphin dance” to professional pilots.
re: now I can’t change my altimeter anymore as well… what the hell is going on?
Sorry but you are at FL310 so the standard barometric setting SHOULD be used. Now, if I’m not mistaken, that is something that the pilot needs to do when crossing FL180. It seems that the flight sim is doing it for you. If you drop back down in altitude to say 17,000 feet you should be able to adjust the barometric setting once more 
Problems with yaw dance with hdg here
I hope that is all the “assist” EASY settings are set to HARD, the sim will not do this !!!
not related with assist settings
You can change the altimeter when going over 18000. Even if it’s not procedure, the sim let’s you change it. I have to set it myself to 29.92 when passes through 18000, because my settings are on realistic. So yeah… that’s why I was on 29.92. Even when I was under 18000 I couldn’t change it.
All settings were on hard, just to confirm.
I have a suspicion they are way over their heads because of the popularity of the sim. ASOBO was a relatively small company before msfs2020. I think their supportdesk and QA teams can’t cope at the moment.
You have to admit, dolphin dance sounds way more catchy 