Motivated by recent zone annealing measurements on stripe-forming block-copolymer films [B. C. Berry, Nano Lett. 7, 2789 (2007)], we study block-copolymer ordering with a spatiotemporally heterogeneous mobility. Specifically, we implement a time- and space-dependent mobility field in the relaxation of a diblock copolymer self-consistent field theory. The model includes a gradient in the local mobility and intrinsic nanoscale mobility variations characteristic of glass phenomenology. The simulations demonstrate that a spatiotemporally heterogeneous mobility can have a significant influence on microdomain ordering in block-copolymer systems, and that nanoscale dynamic heterogeneities associated with glass formation can impact the structure of the ordered block-copolymer microphase.