Looks like the issue is with libpng now. CMake is complaining that it can't find a certain function from that library that's called at some point by Dolphin's code.
You're probably not using the latest version of libpng. Ubuntu 14.04 has 1.2.50 in its repos, but the function png_set_longjmp_fn() was introduced some time in 1.4.x. You'll have to find a way to update libpng.
EDIT: You can always compile from source (simple enough, usually ./configure && make, switch to root (or sudo as Ubuntu does it) and make install) - https://launchpad.net/libpng/main/1.5.14
You're probably not using the latest version of libpng. Ubuntu 14.04 has 1.2.50 in its repos, but the function png_set_longjmp_fn() was introduced some time in 1.4.x. You'll have to find a way to update libpng.
EDIT: You can always compile from source (simple enough, usually ./configure && make, switch to root (or sudo as Ubuntu does it) and make install) - https://launchpad.net/libpng/main/1.5.14