Print/Scan Canon MX860 with 12.04 64 bit

Did you check the canon site for drivers? theyt make deb files for some their devices

I checked but others do not seem to have had luck with those drivers using a 64 bit OS except for a few, and when I try those
methods they do not work. For example:
https://www.ultimateeditionoz.com/forum/viewtopic.php?f=23&t=3567

explains how to use a private repository to get it to work, but when I try it there are errors getting files
from that repository.

This is similar approach:
 http://www.ubuntubuzz.com/2011/06/download-install-canon-printer-driver.html
but does not work for the same reason.

http://osdir.com/ml/ubuntu-bugs/2012-05/msg18758.html
explains another approach but it does not work as well, at least as it is written.

It seems that the PPA ppa:michael-gruz/canon misses the packages for precise.
It should be possible to manually install the oneiric version.

Try downloading https://launchpad.net/~michael-gruz/+archive/canon/+files/cnijfilter-mx860series_3.10-2ubuntu4_amd64.deb and install it.

I followed your idea. Thank you. The last step where you suggest installing the deb package failed
because of a missing dependency.

          After I type:
   sudo dpkg -i cnijfilter-mx860series_3.10-2ubuntu4_amd64.deb
          it says I need nijfilter-common. Do you know where I can download the correct package from?

       Selecting previously unselected package cnijfilter-mx860series.
(Reading database ... 225788 files and directories currently installed.)
Unpacking cnijfilter-mx860series (from cnijfilter-mx860series_3.10-2ubuntu4_amd64.deb) ...
dpkg: dependency problems prevent configuration of cnijfilter-mx860series:
 cnijfilter-mx860series depends on cnijfilter-common (>= 3.10); however:
  Package cnijfilter-common is not installed.
dpkg: error processing cnijfilter-mx860series (--install):
 dependency problems - leaving unconfigured
Processing triggers for bamfdaemon ...
Rebuilding /usr/share/applications/bamf.index...
Processing triggers for desktop-file-utils ...
Processing triggers for gnome-menus ...
Errors were encountered while processing:
 cnijfilter-mx860series

Try:

sudo apt-get -f install

HTH

You suggest I try this?
sudo apt-get-f install cnijfilter-mx860series_3.10-2ubuntu4_amd64.deb

If so, could this break the software system?

Just:

sudo apt-get -f install

On it's own, as I gave it. I never mentioned a deb file.

That completed without error. What would the next step be to get the mx860 working? Is there some written procedure for geting the mx860 to be recognized by my wireless PC?

I had the same problem as you and I followed this tutorial:
http://ubuntuforums.org/showthread.php?t=1488850
And it worked !
What you need to do is simple
go to
http://software.canon-europe.com/products/0010699.asp
get
cnijfilter-mx860series-3.10-1-i386-deb.tar.gz
untar it
$ cd cnijfilter-mx860series-3.10-1-i386-deb/packages
$ sudo dpkg --force-architecture -i cnijfilter-common_3.10-1_i386.deb # You will maybe need to install libpopt-dev before that
$ sudo dpkg --force-architecture -i cnijfilter-mx860series_3.10-1_i386.deb
Go to System Settings.../Printing, press Add, look in Network Printer, wait.... Your printer should appear !
Click on it, press Forward, and the rest is self explanatory :)