Unfortunately, checkinstall's --provides option did not work as expected. So I had to find a way to have them use the manually installed version I compiled from svn and hiding that fact that my package manager. I had to let the package management system know the package was already installed.
So I ended up creating an artificial package that only has the same name and a similar package version, but no actual contents. Create an empty directory, place the following Makefile into it and execute the following checkinstall command. You may need to adjust the parameters for different packages, refer to the output of apt-cache policy somepackage for an appropriate version number)
install -d /usr/local/bin
checkinstall --nodoc --install=no --pkgname=libavcodec51 --pkgversion=3:0.svn$(date +%Y%m%d)-12ubuntu5
checkinstall --nodoc --install=no --pkgname=libavutil49 --pkgversion=3:0.svn$(date +%Y%m%d)-12ubuntu5
checkinstall --install=no --nodoc --pkgname=libavformat52 --pkgversion=3:0.svn$(date +%Y%m%d)-12ubuntu5
sudo dpkg --install ./*.deb
This elegantly fixed the error "ffplay: symbol lookup error: /usr/local/lib/libavcodec.so.52: undefined symbol: av_gcd" and "ffmpeg: error while loading shared libraries: libavformat.so.52: cannot open shared object file: No such file or directory" for me.