Reducing ground level fluctuations when Multiplexing 7-Segment Displays
You can reduce the off time to maybe 1-2 usec most likely, assuming you have push-pull drive of the PNP transistors. 

For dealing with noise, make sure the ground of your ULN2003 is separate from the ground reference of the ADC (probably the ground pin of your micro) and make sure the applied voltage is with reference to the latter. 

The ULN2003 will switch a peak current of 53*7 = 371mA, which is problematic, especially on a breadboard.