The nonlinear Compton scattering by a linearly polarized laser pulse of finite duration is analyzed, with a focus on the spin effects of target electrons. We show that, although the Compton scattering accompanied by the electron no-spin flip is dominant, for some energy regions of Compton photons their emission is dominated by the process leading to the electron spin flip. This feature is observed for different pulse durations, and can be treated as a signature of quantum behavior. Similar conclusions are reached when analyzing the scattered electron energy spectra. This time, the sensitivity of spin effects to the carrier-envelope phase of the driving pulse is demonstrated. The possibility of electron acceleration by means of Compton scattering is also discussed.
