The bug
When the player is flying, the model in the inventory doesn't shifting its body correctly relative to the mouse position. For example, suppose the game is set to full-screen. If your cursor is at the left side of the screen, the model would look towards your cursor correctly. However, if your cursor is at the right side of the screen, the model would be shifting in the opposite direction relative to the cursor.
This issue does not seem to affect the player's swimming pose.
How to reproduce
Equip elytra
Fly using your elytra
Open your inventory menu
Move your mouse around, especially to the left and right side of Minecraft (or screen, if you're playing in full-screen mode.)
Note the model's behavior in relation to the mouse cursor
History of this issue
Originally, this ticket was reported for the inventory screen if the player is dead/dying. However, as of 15w41b, the inventory now closes when you die. It has then been suggested that this issue also occurs when opening the inventory after right-clicking a bed, but before getting into it. This video shows how that looks as of 20w07a: https://youtu.be/1bJgALyjt1Y.
Linked issues
is duplicated by
relates to
Attachments
Comments
What if you're doing something in your inventory, while you're at half a heart left, a zombie came up and killed you, and your mouse is outside of the inventory while you're holding a stack of diamonds?
Especially when the server has settings:
/gamerule keepInventory true
When all of the mentioned above happens, your diamonds will pop out of your inventory, and risk being thrown into a pit of lava, when you can avoid that entirely by not having the inventory GUI affect you when you're holding a stack of items.
It'll become an annoyance for you in the long run.
Thus, I propose that when you die with the inventory menu opened, your model falls down but the inventory doesn't close up immediately. This tells the player that he/she has died, and will take actions upon it.
As of snapshot 13w10b, this problem still exists. Note that when a player dies, the player's skin is reverted back to the default skin.
The bug isn't that the player model doesn't follow the mouse correctly, it's that you can actively use the inventory while dead, as stated above. That means that if you couldn't use the inventory, the bug would be fixed. 🙂
Seems easy enough!
I'm going to let others decide on this issue then. As mentioned, it's really easy to fix this.
Confirmed in 1.5pre. Also the skin is reverted back to default skin when you wait long enough.
Confirmed.

Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
Yes, it's still an issue.
I'll try to keep up.
To the mods:
Can anyone help monitoring this issue? I'm going to start my conscription service soon, and I won't be available to continue tracking this issue. As of now, this issue is still valid.
Thanks in advance.
Confirmed for 08a
Confirmed for 14w11b

Seems to be fixed in 14w21b there is no sneaking animation anymore
Nope, still a problem.

Is this still a concern in the current Minecraft version 1.8.1 Prerelease 3 / Launcher version 1.5.3 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
in 1.8.1-pre3, the dead body still shifts in strange ways based on the cursor.
However, I think the bigger issue is should the inventory stay open when you die, as discussed above. If keepinventory is off, then it should probably close immediately. As for when it's on, I'm not sure what I think. I'll have to do some testing. Is there any way to set that property on a single player world?

It's the same as in Multiplayer, "/gamerule keepInventory true/false".
Ok I don't mess with that stuff ever so I was confused.
I tried setting it to on, and the game told me it was on, but every time I died, it deleted the inventory anyway and dropped the items on the map.
It seems that, now, when you die, you get kicked out of the inventory screen.
However, can confirm with the elytra.
Confirmed for 1.13.1 (elytra).

Affects 19w38b with crawling. Can I request ownership?
Connor Steppie, the ownership is at Microsoft/Mojang at this point.

...so you're Microsoft?

Affects 19w39a

Easiest way to reproduce now, is by using Elytra and open inventory.
Affects 19w42a.
Interestingly, this does not happen when swimming / crawling. Also, it's no longer possible to keep the inventory screen open while dying, so I'll update the ticket's description accordingly.
Here's a video of me trying to reproduce the issue in 20w07a by sleeping: https://youtu.be/1bJgALyjt1Y. Not sure if this still qualifies as an instance of this bug (the player's animation looks fairly reasonable to me).

Affects 1.16-rc1
I'd like to request the ownership of this report as the reporter has been inactive since September 2019.
@Avoma,
I'm still active, and am still receiving email updates from this bug. It's just that, the bug is still there in the game, and I don't know what new information I can provide about the bug.

The thing to do would be to test it in new snapshots and releases and add those to the version list. Since there already is a somewhat recent version added, it's not that important, but it might help a bit. Also, if you wanted to really put a lot of effort into it, you could do a code analysis or tell people in other places to vote for it, but that's about it.
Can confirm in 20w48a.
Can confirm in 20w51a.
Can confirm in 21w03a.
Can confirm in 21w05b.
Can confirm in 21w06a.
Can confirm in 21w07a. Video attached.
Can confirm in 1.16.5 and 21w11a.
Can confirm in 21w15a.
Can confirm in 21w17a.
Can confirm in 1.17.
I actually think this ticket hasn't even been triaged by the team yet. Still hoping they would fix this.
It got priority, so it got triaged.

Can confirm in 1.19.2 and 22w45a.
The rotation of the model when flying with an elytra has something to do with the facing direction. If you fly north, it looks normal, if you fly south, the model is upside down.

Can confirm in 23w06a

Affect 1.20 Re-release 7

Can confirm fixed in 23w31a
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Cannot confirm; this has been fixed prior to 1.20.4 and 1.20.5
Oh nice! Finally, we can put this issue to bed.

I can still reproduce it in 1.20.5
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I updated the title because from my testing the orientation generally was problematic, the shifting in relation to the cursor seemed mostly fine

Can confirm in 1.21.6-pre1
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I think the bug should be that you can access your inventory at all during death. It may be better to simply force the inventory GUI to close upon death, as you shouldn't have access to it until you respawn.