Increase toggling speed of PNP for PWM
Human eyes have a log response, so losing a bit of brightness is a lot less undesirable than some brightness where it doesn't belong. 

The "right" way to do this, in my opinion, is to insert some dead time so that the drivers have a chance to settle out. IOW, turn off the one driver, wait and wait and wait (that's 3 microseconds perhaps) and then turn the (updated) drivers back on. 

How fast are you multiplexing? Don't go excessively fast, there's no advantage. The 74HC595 is a push-pull output and it will suck the charge out of the base of the PNP pretty fast as it is. You could try ~100pF across R2 or (!) a Schottky clamp diode from the collector to base, but we're talking a visual display here, presumably, so that's a bit silly. 

Edit:
The 100pF is called a "speed-up" capacitor. It allows the 74HC595 p-MOS transistor to remove the base charge more quickly. Ideally it has a a value to give a rectangular waveform as shown below- 0.1uF is too large, you should need no more than a couple hundred pF. This page is well worth reading, and below image is taken from there. See also this answer. 



You need one per transistor, same as the resistors. If it's SMT you could retrofit by putting a small cap literally on top of the resistors.