"Is it only I who thinks, that the lateral stability feathered and unfeathered does not look great in those videos? "
Lateral, and longitudinal; I wondered too. The first thing that came to mind was "PIO".
It occurs on all flights I've viewed the videos for so it's not unique to one flight.
I would think you'd still want to dampen it before serving the bubbly...
In the aft-view video above, I looked for small movements of controls but couldn't discern any although they'd probably be tiny. And oscillations don't stop except briefly at two points: approach to the apogee, and later in the descent when the feathers retract to normal position.
BOAC, gums, Retired4 - if you can look past the soft stuff in this early commercial for Virgin Galactic, there's something of an explanation regarding the feathers @ 2:40 in this video, (which also shows the wing-rocking at the beginning of the video for a flight in October, 2004).
https://www.youtube.com/watch?v=MN-GE4D61Zk
Beginning at 00:45", another video, (first flight with "feathering"), shows what I would call a "significant" pitching & rolling pre-, during and post-feathering.
https://www.youtube.com/watch?v=Lqhzlq7UReA
janrein;
Re, "
Of course the unburned fuel mass after premature motor-stop is an additional weight/energy burden for reentry, the loaded SS2 is 30kLB (AWST), how much of that is the fuel mass? And can the oxidiser be dumped (through the extinguished engine) without re-lighting it? "
At 1:20 in the video with the aft-looking camera linked in the post above there's a crew remark, "auto-dump" and a cloud of gas is seen leaving the ship; it occurs again at 02:30 into the video and I suspect that's unburnt fuel and/or oxidizer. It doesn't appear to be dumped from the engine from from behind the tail-camera.