Any compression of a video will degrade it slightly. That is a maxim in video encoding. But it isn’t really that simple.
In general, compressing a video will reduce its quality if you use the same codec in compression. For example, using DVDShrink to reduce the size of a dvd-video will definitely have an impact on the quality of the movie. Whether or not you see that on the screen depends entirely on how much compression is used, and the nature of the movie. If it is mostly set pieces, with little action, you probably won’t notice as much as film with a lot of motion sequences.
You must also take into consideration, the type of compressor you are using. DVDShrink is a transcoder and is inferior to that of a full encoder in its output, especially on video that needs a lot of compression to fit a dvdr. If you use an encoder, like HC or CCE or ProCoder in DVDRebuilder, the overall quality will be better than Shrink, but still slightly less than the original. There are technical reasons for this, and if you are interested you can google the differences between mpeg2 transcoders vs encoders.
You can also go to a different type of codec, and still maintain high quality at much, much smaller file sizes. This is one of the reasons for development in xvid, divx, VC-1 and H264. The newer codecs are much more efficient in compression than mpeg2.
If you have to maintain quality, with no compromises, then going to a disk with larger capacity is the way to go, or split the movie/video onto two single layer dvds.