Update, NUM6 fixed the problem! Adding a 1kohm resistor seemed to fix all the problems. But I will still post a more detailed answer to the problem. Hopefully it will help others.
1) Yes. That is what happens. Here is a video of this occurring.http://www.youtube.com/watch?v=4EbHU4AgEs0&feature=youtu.be
2) This is a 128x64 display
3) The part num is GDM12864HLCM from SparkFun
4) The library has not been altered for the Uno. However manual pins were set for the Mega as one of the ports on that controller was found to be bad.
5) The two green wires go to a 10k potentiometer. Which is read by A5.
6) There was nothing previously. CONNECTING THE RESET PIN TO VCC WITH A RESISTOR SOLVES THE ISSUES
7) The number of wires attached does not effect the display performance. The test in 1) was done using the setup from 7).
--Thanks for helping me figure this out Bill!