The family of three-dimensional topological insulators opens new avenues to discover novel photophysics and to develop novel types of photodetectors. ZrTe₅ has been shown to be a Dirac semimetal possessing unique topological electronic and optical properties. Here we present spatially-resolved photocurrent measurements on devices made of nanoplatelets of ZrTe₅, demonstrating the photothermoelectric origin of the photoresponse. Due to the high electrical conductivity and good Seebeck coefficient, we obtain noise-equivalent powers as low as 42 pW/Hz^1/2 at room temperature for visible light illumination at zero bias. We also show that these devices suffer from significant ambient reactivity such as the formation of a Te-rich surface region driven by Zr oxidation, as well as severe reactions with the metal contacts. This reactivity results in significant stresses in the devices, leading to unusual geometries that are useful for gaining insight into the photocurrent mechanisms. Our results indicate that both the large photothermoelectric response and reactivity must be considered when designing or interpreting photocurrent measurements in these systems.