EDIT: As @wimpy states in post #2. The packages are updated. I will keep this here if you experienced this issue.
Just to let you know. I used the flexiondotorg ppa to install Minecraft manually on another computer and got an error message stating that favicon.ico could not be downloaded as it had been permanently moved, resulting in a 301 error message from wget.
It appears that the Minecraft.net website got an overhaul and the icon can now be found at:
https://minecraft.net/static/theme/img/favicon.59b38b30b38a.png
Just for when there is some time to change it.
A workaround:
I thought I had a nice workaround, but I kept getting the same error message over and over again, so I had to do some hacking 
But it worked!
First install Minecraft using the Software Boutique and then open up a terminal (F12 for tilda wil do just fine) and do the following:
cd /var/lib/dpkg/info
sudo pluma minecraft-installer.postinst
Find the following line:
MINECRAFT_ICON_SRC=http://www.minecraft.net/favicon.png
And change it to
MINECRAFT_ICON_SRC=https://minecraft.net/static/theme/img/favicon.59b38b30b38a.png
Edit 8/2/2016:
The line should read the following now:
MINECRAFT_ICON_SRC=https://minecraft.net/favicon-96x96.png
After that run:
sudo apt-get install -f
This will remove the error message and Minecraft will install nicely
