Maximum speeds Vmo/Mmo
 

So I understand that Vmo is associated with lower altitudes and takes into consideration structural loads and flutter, while Mmo is associated with higher altitudes and deals with compressibility effects (and flutter as well). My question is, for example, the CRJ-900, why does Vmo go from 330 (0-8000) up to 335(8000 - 25600) and then down to 315 (28300 - 31600) and Mmo goes from .80 (25600 - 28300) to .85 (31600 - 34000) to .84 (34000 - 41000)? Is there a simple explanation?

Below 8000ft there are rules for birdstrikes. Many aircraft have lower speeds at low altitudes to make it easier for the aircraft to resist a bird.

The strange shape around 30kft is all to do with controlling the "corner point" of max V and max M at the same time. The numbers you quote give three "corners" to the Vmo/Mmo graph around there:

25600ft - 335 KIAS - M0.80
28300ft - 315 KIAS - M0.80
31600ft - 315 KIAS - M0.85

If instead it was "simplified" to be just 335KIAS up to a crossover with M0.85, that combination of 335KIAS and M0.85 is more challenging for various design requirements. Turns out, it's not important enough to do the extra work to have that performance, and the displays keep track of Vmo/Mmo for you so there's no extra workload. So it's done to make the design easier (or cheaper, if you like)

The M0.84 cutback at high altitude is I think supposed to be explained in training. If you have access to a 70 manual, compare it - slightly different cutback speed. Subtle differences in aircraft handling behaviour, the cert rules and no overriding need to be at such speeds (its above normal cruise speeds) leads to the cutback.