Song Connections
First off, the really obvious Tucson Diagnostics tying together all of Artificial Heart. By the way, I went snooping around the internet, and though I'm not 100% certain, I'm pretty sure that all of the Tucson Diagnostics materials out there were made by Jonathan Coulton for the album, it is not an actual organization.
Now onto more subjective stuff! 
I like to think that the person singing Overhead is singing to the person who sung My Monkey (and that Overhead comes chronologically after My Monkey).