Web cam tell to do nologin
I'll check further to see why motion could be trying to log to that location. First you could try creating a file called there and then change its ownership to www-data (sudo chown www-data:www-data /home/pi/motion.log). The all were running for month now without problems.
The current repository should carry a version that's running smooth under a fully updated raspian (also do rpi-update). Raspimjpeg makes use of the officially added tools/kernel drivers in raspbian for the camera/GPU, as far as I know.
The wiki How Tech Team also followed the article's instructions and validated that they work. This wiki How teaches you how to install and set up a webcam on your Windows or Mac computer.