At this moment, I have driven several hundreds of kilometers in different driving conditions, and I’m ready to share my first impressions.
Subjectively, the DME works correctly. Switching between injection modes and NOx converter regeneration sessions is happening softly and imperceptibly. Misfires or rough engine performance when switching between injection modes was not observed.
Several differences from MSD80 (with the last ZB release and DIRU):
a. in idle, Stratified charge tries to maintain Lambda around 1.80, which is slightly lower than MSD80;
b. regeneration sessions are happening more often than for MSD80, not taking into account the perfect NOx data. Obviously, BMW engineers have lost part of the optimism regarding the real performance of the NOx catalytic converters. In addition – after a larger required torque, DME assumes that the NOx catalytic converter is partially contaminated (quite a logical assumption) and first regeneration is required swiftly after switching to Stratified charge;
c. the math for creating the injector/multiplicative-type (flowrate) adaptations of the banks has been changed. Previously, there were several problems with the injector flowrate, even in the case of correct multiplicative-type adaptations of the banks. MSD81 created correct flowrate adaptations for the injectors:

d. it is interesting that the flowrate data, measured in Stratified charge mode (../F5/Shift+F6/5, lines 7 to 12), are no anymore immediately applied to the injector flowrate (../F5/Shift+F6/F1, lines 4 to 6) during Stratified charge. More exactly, they are not applied to the 2nd impulse (the one that can be seen with INPA). It is possible that these test results are applied to the 1st impulse (it can not be seen with INPA) or – uniform coefficients of Stratified + Homogeneous mode are applied. I will explore this feature in more detail;
e. Rough run data (../F5/F7) indicate a very stable idle, although subjectively, the stability of the idle is not very different from MSD80. It turns out that the “sensitivity” of the MSD81 in this menu is reduced! Obviously, BMW engineers continued the fight with the fake 3104 error messages.

In the image above: cylinder No.1 is switched off; the engine works on a Stratified charge. For MSD80, in this situation, the bar of the 1st cylinder indicated around +7 units. Here, as we see: only around +3.5 units.

In the two images above: cylinder No.1 is switched off; the engine works in Homogeneous mode. Unfortunately, in this mode, Rough run algorithms are working incorrectly. Very often, DME identifies increased(!) mechanical efficiency of the switched-off cylinder, which is not real. There is a feeling that the code from some very old MSD80 release has been put in copy/paste. It means that the identification of misfires (in idle, Homogeneous mode; at this moment, I have no information regarding other modes) will be burdened.

Not just criticism: below are some images that are close to perfection:

In the 2nd bank: relatively new injectors. As we see, both Offset and Multiplicative type LTFT are perfect. In the 1st bank – injectors with a resource of at least 200’000 – 300’000 km. Here, too – Offset LTFT: perfect.
Injector data in Stratified charge:

The injector of the 2nd cylinder is slightly dripping, but – at the same time: the cold start was perfect;

Injector flowrate adaptations: perfect.
Injector tests in Homogenous mode:

Test results – close to the ideal.
Idle smoothness:

In the image above – Homogeneous mode.

In the image above: Stratified charge.
Note: MSD81 has reduced sensitivity in this menu. 0.1 units correspond to around a 3% mechanical efficiency difference from the ideal.
A final note: the resource of this engine – more than 800’000 km!