Multiplexing a big 7-seg display with MAX7219
I think the problem is that the segment drivers are not push-pull, rather they go high-impedance when they are turned off. Since the darlingtons in the UDN2981 will turn on with some tens of uA it will take some time for them to turn off. Since your brightness is so high for the 'on' segments, the 'ghosting' is significant. 

Try a pull-down resistor on the inputs to the UDN2981 (try it on one first and see if the ghosting goes away in the one segment position).