Polarization-sensitive global VLBI observations of the BL Lacertae object 0735+178 have been made at epochs 1987.41, 1990.47, and 1992.44. Comparison of the resulting images with previously published VLBI images of this source confirms superluminal motion of one component (''K2'') at a speed 17.4 h(-1)c. We have identified two additional superluminal components with apparent transverse speeds greater than or equal to 5.0 h(-1)c and greater than or equal to 4.2 h(-1)c. The images presented here span a period of time during which K2 should have collided with a nearly stationary component (''K1'') at a distance similar to 5 mas from the core; our images show no evidence of a violent interaction between these components, supporting the possibility that K1 represents a local region of enhanced emission in an underlying flow, rather than a physically distinct ''blob'' of relativistic electrons traveling outward from the core. VLBI polarization images for 0735+178 are now available at four epochs; at three of these epochs, the integrated and milliarcsecond-scale polarization are appreciable, but at epoch 1987.41, both the integrated and milliarcsecond-scale polarization are very weak. The available VLBI polarization data and integrated monitoring data suggest that this unusual weak milliarcsecond scale polarization was associated with the formation of a new transverse shock, and near cancellation of orthogonally polarized emission from quiescent and shocked material in the VLBI core.