Well, it's progress anyway. At least dvdstyler is no longer complaining about wxgtk.
I had the same problem, and solved it with links. It's looking for libavformat.so (a file in ffmpeg) but the number is wrong. With Gslapt, check out the ffmpeg package you have installed, specifically the "files" tab, and see what number the file libavformat.so has. On mine, it is libavformat.so.53.31.100, so I made a link of the file it was requesting to this file that is installed, and it worked. For clarity, see my enclosed screenshot.
So, try the following (replace the numbers with whatever numbers you find in the listing of file "libavformat.so.**" in ffmpeg within Gslapt):
ln -s /usr/lib/libavformat.so.53.31.100 /usr/lib/libavformat.so.52
Note, since the error you were getting was requesting "libavformat.so.52", I put this as the created link above. Again, it should link to whatever version of libavformat.so is listed under files of ffmpeg within Gslapt.