Automated removal
skip to the bottom of this answer for a scripted way to remove offending software-sources
The 404 or Not Found error message is a HTTP standard response code
indicating that the client was able to communicate with the server,
but the server could not find what was requested.
The web site hosting server will typically generate "404 - Page Not
Found" web page, when users attempts to follow a broken or dead link.
What are the causes of these errors in update-manager
Typically, three main areas cause these errors in update-manager
- A user has just upgraded and has re-enabled a PPA software-source that no longer exists

- A user has manually typed in a new software source incorrectly

- A PPA was added, but the maintainer has subsequently deleted some/all of the PPA
where are these software-sources
PPAs typically are saved in one of two locations
/etc/apt/sources.list
- in an appropriately named file with a .list file-extension in
/etc/apt/sources.list.d/ for example webupd8team-jupiter-natty.list
This list file typically contains:
deb http://ppa.launchpad.net/webupd8team/jupiter/ubuntu oneiric main
# deb-src http://ppa.launchpad.net/webupd8team/jupiter/ubuntu oneiric main
Note a # at the front of a line of text means that it is commented out and is not checked by the package manager.
How to eliminate these errors
Typically, if you run sudo apt-get update from a terminal or click the details button in Update Manager after hitting the refresh button you will see errors such as:
If the error is due to a PPA - usually unticking the similarly named PPA with the URL shown in the error message will resolve this.
If the 404 error was due to an additional repository that has been added to /etc/apt/sources.list then its easier to add # character to the start of the line to comment out the offending repository i.e.
gksu gedit /etc/apt/sources.list

Scripted removal
I've written a quick script that checks for PPAs and Software-Sources that exhibit the 404 errors.
Its in my PPA:
sudo add-apt-repository ppa:fossfreedom/packagefixes
sudo apt-get update
sudo apt-get install banish404
You can just download the deb package and install that directly:
wget https://launchpad.net/~fossfreedom/+archive/packagefixes/+files/banish404_0.1-4_all.deb
sudo dpkg -i banish404_0.1-4_all.deb
N.B. its the same deb package for all distributions.
Questions/Comments/Improvement please via Launchpad Contact Me link
How to use:
sudo banish404
The script will automatically backup of your sources before modification - to be found in /etc/apt