It seems that new Opera has a dependency problem with libdbus-1-3 in the DEBIAN/control file. Opera 52 installation fix is to edit that file by removing (>= 1.9.14) after libdbus-1-3 and then build a new package. An example about building the fixed package:
1. Extract an original package
2. Edit DEBIAN/control file
3. Build a fixed package from a edited package
sudo chown root:root -R build-folder
sudo chown root:root -R opera-stable_51.0.2830.40_amd64
sudo dpkg -b build-folder fixed.deb
sudo dpkg -b opera-stable_51.0.2830.40_amd64 opera-stable_51.0.2830.40_amd64-fixed.deb
Probably automatic opera-update does not work with Mint 17, so you need to upgrade Opera by hand.
The same issue and fix works also with Linux Mint Debian (LMDE).