'apt-get update' isn't going to tell you much
by itself. You'll just see a list of the repos it hit, and what it synced to the repos. You WILL see if hitting a particular repo failed; if that is the case, there is a problem on the server end, not in your box. You can change the repos to other regional servers in /etc/apt/* if you look at the official repo list available from Debian.
If what you want to know is what is to be installed, there are other commands that will be very verbose about what apt-get wants to do.
Run 'apt-get update' first. Then, take a look at 'apt-get dist-upgrade -s'. This will tell you exactly what apt-get wants to upgrade to bring the system up to date, and what it wants to remove [if anything]. The output is quite clear, and will provide version numbers. The '-s' argument is 'simulate', so it won't actually install anything. To perform the installation, run it without the '-s'. To download the needed packages ONLY, but not install them, use '-d'.
Apt-get is very, very smart. It knows what you have installed already, and makes decisions on what is important to update and what sequence to update the packages in.
If you have a problem with a broken package, 'apt-get install -f' will normally fix the issue. This scans your system for dependencies and will resolve any conflicts.
Remember that Synaptic is a GUI front-end for apt-get anyhow, so to learn to use all the options of apt-get at the command line is a *good thing*. There is no reason to be afraid of it. Any command that you use with apt-get can be followed by '-s', so it displays what it wants to do
only. Then, you re-run the command without the '-s' if you want to do it.
I learned to update my Sid installs regularly this way. Because Sid is Debian's unstable branch, it would not be possible for me to maintain its moving target using Synaptic. TBH, the way apt-get outputs the information is MUCH more concise and easy to understand than using Synaptic.
The 'Gtk-CRITICAL' output you're getting is related to libgtk; there are ALWAYS a number of open bugs in Linux distros regarding this. You might try searching the bugtracker but sooner or later it will be corrected. It is usually a versioning/dependency problem that showed up after a new libgtk version is released. I see this quite often in Sid and also in Gentoo. Gtk stuff is related to the GUI and themes; using apt-get on the command will take libgtk out of play. Don't forget what I said before,
that Synaptic is simply a GUI front end for apt-get.
Here is the apt-get man page:
http://linux.die.net/man/8/apt-get