Reproduction:

Create a freestyle job. As only build step, have a Windows batch containing "set". Run and inspect the console output, look for the PATH environment variable.

Result:

Jenkins wrongly uses quotes when adding the current JRE path, e.g. in my case the PATH is shown like this
Path=C:\Program Files\Java\jre6\bin;C:\Windows\system32;C:\Windows;C:\Windows\System32\Wbem;C:\Windows\System32\WindowsPowerShell\v1.0\;C:\Program Files (x86)\Git\cmd;"C:\Program Files\Java\jre6\bin"

Every command which tries to modify the path during a Jenkins job will fail because of those wrong quotes, e.g. you can no longer run batch commands like

setx PATH "%PATH%;c:\some\new\path" /m

because the quotes are incorrectly nested.

Running "set" outside Jenkins produces the same path without the quoted JRE path.

Jenkins version 1.527