Is there any residual oscillation left from the Moon rotation? The Moon is tidally locked to Earth - a long time ago it was spinning, but after a time, the spin stopped - two factors stabilizing it: unequal mass distribution creating an equilibrium position where there's one "preferred" axis by which it faces Earth - an attractor, and the dynamic tidal forces acting as stress upon its structure, dissipating the energy - a friction, reducing the rotation speed.

So, at one point in time, it would no longer complete a full spin, but instead reverse its turn direction, start spinning in opposite direction, with maximum spin speed around the time where the "preferred" axis faces Earth, then slowing down again, until its spin stops, and reverses direction again - each time the angle smaller as the dynamic forces act against the direction of rotation - but also, with the rotation angle and angular velocity dropping, the value of the dynamic forces dropping.

There is a significant apparent wobble caused by the orbit's eccentricity, and possibly some actual continuous wobble, as the result - with the attractor axis missing Earth as result. But is there any long-term oscillation left over from the times when the Moon was spinning - a harmonic motion around its original spin axis, that would likely not be in tune with the orbital period? (I imagine the period of these oscillations would be very long; after all it's about reversing Moon's spin back and forth, by a force that isn't all that strong.)
This is called "physical libration". The Moon’s physical librations and determination of its free modes (2011) estimates it using the Apollo mission retroreflectors. Their result is very small. They note that the "damping times for these two modes are estimated as $2$x$10^4$ and $2$x$10^6$ years", so it is a mystery why it is even as large as their small result. They say:


  Some possible excitation mechanisms have been explored in the past without satisfactory explanation. It has been shown that a recent meteoroid impact is an unlikely source of such excitation Peale (1975). Eckhardt (1993) proposed an excitation process related to a resonance crossing of the longitude normal mode (of 2.9 years) and a close forced frequency. During the evolution of the lunar orbit, the free and forced frequencies change slowly and can cross. However, the mechanism excites only the libration in longitude mode. Yoder (1981) proposed an alternative mechanism, based on turbulent fluid core interaction, to excite the wobble mode. The new determination of the amplitudes of the free librations invites new investigation of their excitation mechanisms.


I did not search to see whether anyone has taken up their invitation.