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Materials exhibiting reduced dimensionality and strongly interacting charge and lattice degrees of freedom, such as layered transition metal dichalcogenides, can appear in various atomic structure states that harbor fascinating quantum phenomena. The complexity of the states, however, often makes it challenging to identify the nature of the observed phenomena, impeding their exploration for practical applications. We show that the problem can be alleviated by using high-energy x-ray diffraction coupled to atomic pair distribution function analysis. In particular, using this non-traditional technique, we find that whereas, macroscopically, the reversible transition between the polar 1T’ and non-polar T_d phases of MoTe₂ is first-order, locally, it is not. A great deal of the stacking sequence of Te-Mo-Te layers characteristic to the polar 1T’ phase persists locally in the non-polar T_d phase, and vice versa, over a broad temperature range extending about 100 K both below and above the transition. The presence of coexisting local polar and non-polar regions and the resulting variety of internal interfaces where the spatial inversion symmetry is broken may be behind some of the unusual electronic properties of T_d-MoTe₂, including its putative type-II Weyl semimetal state.