Ubuntu – Not all updates can be installed, partial upgrade proposed

Yes, do try and run

sudo apt-get install -f

From the --help usage text we find

-f  Attempt to correct a system with broken dependencies in place

You can get to this by using

apt-get install --help

Another good way to read up on usage is with man pages. The man page for apt-get states

-f, --fix-broken
       Fix; attempt to correct a system with broken dependencies in place.
       This option, when used with install/remove, can omit any packages
       to permit APT to deduce a likely solution. If packages are
       specified, these have to completely correct the problem. The option
       is sometimes necessary when running APT for the first time; APT
       itself does not allow broken package dependencies to exist on a
       system. It is possible that a system's dependency structure can be
       so corrupt as to require manual intervention (which usually means
       using dselect(1) or dpkg --remove to eliminate some of the
       offending packages). Use of this option together with -m may
       produce an error in some situations. Configuration Item:
       APT::Get::Fix-Broken.

There's nothing wrong with running the partial upgrade, incidentally, it generally fixes the problems in the package manner. Please let me know if you continue having these problems afterward. Best regards

Package: *
Pin: release a=precise-security
Pin-Priority: 990

Here, there is a problem. Security packages always have higher version string. Always. You don't need to set package pinning to prefer those packages. APT will always install the higher version available unless any user preference restrict this behaviour, which is what you are doing.

I don't know what you want to achieve with those package pinning, but they will give you headaches. Package pinning was designed for different packages sources (i. e. Ubuntu and some sort of PPA) and is normally preferred to manipulate the priority of the non-official source. The proposed repository always has lower priority, the security repository always has automatic upgrades daily.

I recommend you lower the PPA priority (if it's that what you want to control) instead of modifying the Ubuntu repositories.

If you don't want to change anything, you can force apt to bind to your wishes using:

sudo apt-get install libxi6=2:1.7.1.901-1ubuntu1~precise1

or

sudo apt-get install libxi6/precise-updates

But remember that the updates repositories always will have all the changes made by the security repositories.