I've first written a script that make the Raspberry Pi autonomous for taking videos when the device is powered. It records videos, give them a proper name and delete the oldest of them if the sdcard is near full.
Then I tried to install the device into my car. I hadn't planned a place for it but I found a nice one I hope. Here is some pictures of my advancements :

The camera is visible above the rear view mirror. It is rather well hidden.

I've put the Raspberry Pi here, I had to remove the interior lights though :/

The installation is rather temporary, maybe I can hide that mess a little better but it's not so bad. The camera cable goes between the plastic case and the roof of the car.
Finaly I drove my car around and the Raspberry Pi took a video. I'm quite satisfacted with the quality, the video isn't shaking and the resolution is good at 1080p. The field of vision is a little low maybe and I don't know how the capture will do in the rain as it seems my screen whipers don't reach high enough to clean where the camera is.
I will try to make a more permanent installation for this project after more testing as it seems to be working well.
I've got some questions then. I can play the recordings with omxplayer and vlc but I haven't found a working video editor. Virtual Dub and Windows Movie Maker won't open them even after I installed ffdshow. What should I install for that ? Also, is there a way to acces the sd card main partition on windows ? I tried to install Ext2Fsd but it won't recognize it after I plug the card. Well there are some more tools I should try.