Ttyjfyk

I downloaded the installer from the website. When I run it, I get the following error:

Your system has broken dependencies. This application cannot continue until it is fixed. To fix it, run "gksudo synaptic" or "sudo apt-get install -f" in a terminal window.

I tried both options. When tried to fix the broken packages in synaptic I get

Some packages could not be retrieved, do you want to proceed?

I said yes. Then

>E: Unable to correct missing packages
W: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/t/tiff/libtiff5_4.0.2-1ubuntu2.1_i386.deb
 404 Not Found [IP: 91.189.92.201 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/g/gnutls26/libgnutls26_2.12.14-5ubuntu4.2_i386.deb
 404 Not Found [IP: 91.189.92.201 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/m/mysql-5.5/mysql-common_5.5.29-0ubuntu0.12.10.1_all.deb
 404 Not Found [IP: 91.189.92.201 80]
W: Failed to fetch http://security.ubuntu.com/ubuntu/pool/main/m/mysql-5.5/libmysqlclient18_5.5.29-0ubuntu0.12.10.1_i386.deb
 404 Not Found [IP: 91.189.92.201 80]

There are several layers of problems, and they have little to with skype. Any install/update of packages on your system could have triggered this.

If you put your browser to http://security.ubuntu.com/ubuntu/pool/main/m/mysql-5.5/ (url from the last error message without file name), you see that there now are different versions for libmysqlclient*0ubuntu0.12.10. So there is no problem with reaching the server (i.e. it is online), just with your own machine not being up to date.

Normally you should do a regular (daily e.g.) update of the view your machine has of which packages (and their versions) are available with:

sudo apt-get upgrade

the servers do not change that often that it is necessary to run that before every install, but it is a good practise to try and do so if there are problems.

After that run:

sudo apt-get install --fix-missing --fix-broken

and try again.

That problem typically occurs when your local package list cache is out of date. To update it, use apt-get update. After that, you should be able to install the dependencies via apt-get install -f.

It seems you have some broken packages .So to remove it , first try :

sudo apt-get clean
sudo apt-get autoclean
sudo apt-get remove
sudo apt-get autoremove

This will cleanup your system and remove all the unmet dependencies.
Now try using :

sudo apt-get update

Now try using :

sudo apt-get install "package name"

The dpkg error occurs due to 2 problems :
1) You must be using only "apt-get update" instead of "sudo apt-get update"
2) You try to use the installer multiple times that is you try to simultaneously install 2 files on the system.

However I suppose the above suggested method solves your problem , However the easiest way to install skype on linux mint is as follows :
1) Press windows button
2) Type mintinstall
3) The Linux Mint store will open .
4) Search for Skype and Install it .

I installed skype through the 2nd method and feels it is much easier than using command line (if you are a beginner) .