Firstly, RPi-Cam-Web-Interface and therefore DietPiCam is pretty badly broken under Raspbian Jessie and seems to need a lot of reconfiguring on the fly to get it going. Things seem to have broken on the webserver side in both Apache and Nginx as well as in PHP. Default directories have changed and permissions and security settings have been screwed around with.
I haven't gotten the chance to try out DietPiCam on DietPi-Wheezy yet, but I did install the full RPi-Cam-Web-Interface (on a full Raspbian-Wheezy) from the official GitHub repo (testing it under both Apache and Nginx options) and it pretty much worked straight away, without any fuss.
The one major problem I am still having is in getting motion to detect movement and trigger a recording.
I tried the suggestions laid out in the Troubleshooting -> Motion Detection section at the bottom of the wiki page (http://elinux.org/RPi-Cam-Web-Interface ... _Detection) but, although I got stop messages on shutdown, was unable to get the thing to trigger a start event at all.
I was all set to give up on it entirely (for today, at least) when I thought I'd have another try at it's experimental, internal motion detection method. It worked! (It, however, did not work on DietPiCam last time i tried it.)

I'll give it another try, but in DietPi-Wheezy this time, ASAP.
Looking at http://www.lavrsen.dk/foswiki/bin/view/ ... ningMotion I figured that this might be a good way of getting Motion configured, but alas, I hit a dead end there as well; It wouldn't detect the camera. :evil:
If it could be made to work with RPiCam/DietPiCam, this might be a great help.
I'll leave it there for the moment, but hopefully this will help with the diagnosis.
Rich.