We present dielectric and anelastic spectroscopy measurements of the molecular piezoelectric TMCM-MnCl3 and TMCM-Mn0.95M0.05Cl3 (M = Cu, Fe, Ni; TMCM = trimethylchlorometylammonium), whose powders were pressed into discs and bars and deposited as films on Si by Matrix-Assisted Pulsed Laser Evaporation (MAPLE). As in other molecular ferroelectrics, the dielectric permittivity ϵ′ drops at the structural transition temperature TC, below which the number of directions that the polar TMCM molecules visit is reduced, with the formation of ferroelectric domains. Concomitantly, the Young’s modulus E starts increasing and the elastic energy loss has a step-like increase, attributable to the motion of the domain walls. Both the dielectric and elastic anomalies indicate the improper character of the ferroelectric transition, where the ordering of the molecular orientations is not driven by the cooperative interaction of their electric dipoles. Below room temperature, at least two thermally activated relaxation processes appear both in the dielectric and anelastic spectra, whose real and imaginary parts measured at several frequencies can be fit with the Havriliak–Negami formula. The microscopic parameters so-obtained indicate that they are due to point defects, and it is argued that they are Cl vacancies and their complexes with TMCM vacancies. The considerable width of these relaxation maxima is explained by the geometry of the hexagonal perovskite structure. The partial substitution of Mn with 5% Ni has little effect on the anelastic and dielectric spectra, while Cu and, especially, Fe cause a large enhancement of the losses attributed to domain wall relaxation, with substantial contributions also above TC. The condensation of water from the humidity in the powders compacted by cold pressing was observed and discussed. The piezoelectric activity of the films was assessed by PFM.