A GNOME Software update that fixes the issue with installing third-party deb files was pushed to the Ubuntu 16.04 Proposed repository a few minutes ago.
Ubuntu 16.04 shipped with a pretty nasty bug (see here and here): GNOME Software (rebranded as Ubuntu Software in Ubuntu with Unity) doesn't allow installing third-party deb files, like Google Chrome, Google Talk Plugin, the Mega client and so on.
A fix for this has been pushed to the Ubuntu 16.04 Proposed repository and will be promoted into the main repositories once it's tested.
Other changes available with this GNOME Software update:
- support for apt:// URLs;
- increased the number of displayed reviews from 10 to 30;
- GNOME Software now displays version and size information for non-installed applications;
- enabled the Snappy backend.
Those interested in testing the latest GNOME Software from the Proposed repository should see THIS page. Note that the Proposed repository is for testing purposes only and may introduce instability! Also, the option to enable the Proposed repository was moved to the "Developer Options" tab in Software & Updates in the latest Ubuntu 16.04.
Until the update is available in the main repositories, you can use GDebi GTK (or dpkg via command line) to install deb files. Check out our Things To Do After Installing Ubuntu 16.04 article for how to install and set GDebi GTK to open deb files, along with other tweaks.