ZDoom

Just so this doesn't go unnoticed by me:

I will test this at home (i use LZDoom and my PC does not support OpenGL 3.3 AFAIK) and if it behaves the same way, drfrag should be noticed as well.

This needs to be reopened.
In GZDoom 4.5.0, enabling mouse smoothing in options doesn't make a difference anymore.
The recent NightmareLogic by Dr_Cosmobyte exhibits this problem as well, so I'll use it to showcase the problem.
It's only 811 KB in size, all you have to do is download the mod, type IDFA and select the plasma gun.
It uses SPF_INTERPOLATE in its Ready state.
Lower i_timescale to make it more noticeable.

Mod's @ viewtopic.php?f=43&t=70984

[streamable]hn7k41[/streamable]

Recorded footage for your convenience.
I only recorded @ 30 FPS, so in reality it's actually much worse.

This thread title is very misleading. What's going on here is that it's suddenly switching from ZDoom's weirdass method of smoothing mouse movement without interpolation to just simply using interpolation, and this causes it to rubberband.
Turning the "Smooth Mouse Movement" option on "fixes" it because literally all it does is force mouse movement to always use the very same interpolation that SPF_INTERPOLATE uses.

Huh... so it really was broken all this time. Well that explains things...

Using A_SetPitch on its own (for example in a firing state as recoil) works flawlessly, but appending the SPF_INTERPOLATE flag to it causes the view to jump when turning with the mouse during the duration of the pointer, as if the screen updates with 35Hz. This doesn't happen when turning with the keyboard, however. It also doesn't occur if "Smooth Mouse Movement" is set to on. This can be experienced in every mod where that flag is present, for example Trailblazer, Wildweasel's Mixed Tape Vol. 3 and older versions of Final Doomer.