I have graphed each voltage point for a 10 bit ADC, there is noise clearly visible in this graph. How do you reduce noise? From the DAC to the ADC is a short wire about 1 inch and the circuit is properly decoupled. The microcontroller goes into sleep mode during the ADC conversion which helped with some noise. The circuit is an ATMEL tiny26 with a 16 bit DAC controlled by an ATMEGA 162. In the graph, the straight line is the ideal reading the bendy line is the actual reading. The second graph is zoomed in to the first 50 samples where you can see how unacceptable this noise is.

Also, the circuit is on a solderless breadboard, can that have a large effect on noise?
The range on the graph says 0-1023, it does not say the voltage range that is 0-250mV. The file is a zipped XLS graph