Today I found an issue where WebUnit would throw mysterious errors. After some digging, it turned out that the system running WebUnit did not have permissions to use the command line, so it could never launch the web driver.
In the code of InstallWebUnit[] there is the line Quiet[URLFetch[webDriverBaseURL<>"/status"]] that checks if the process is already running. Maybe this check should be performed again after launching the driver to check if it really did launch.