I'm one of the guys with 20 modules that has been doing a lot of testing trying to see what works to get the artifacts off the Parola displays. And I'm posting to say that I was pretty much convinced if the display suffers from that, I was stuck with it. However after a lot of hours of "tweaking", I have a work around that I use.
To start with, after doing everything from building tri-state buffers (to inhibit the signals from a cold boot), triggers to clean up the wave forms, pull-down resistors, and generally mucking around in the MDMAX library, and using my scope to make sure all was well, I found that if I disconnected the Vcc after the Arduino booted up (I'm using a MEGA 2560), then reconnected Vcc and do a soft reset on the Arduino, the crud was gone. Every time. If you try this you'll probably find that once running even when you disconnect Vcc, the displays will stay on. Something isn't right there and I believe that's a "clone" chip problem.
I also found that I needed to add 10+ modules before any artifacts ever showed any way. The artifacts were also random. The best way to force them to appear, power down the Arduino and power it back up within a few seconds. If I let it sit for a few minutes and powered it, I got "luckier" and had less artifacts. Sometimes this lead me to believe I'd found the magic cure. Nope.
So in programmer speak I came up with YAWA based on how I noticed the displays did work. Yet another work around.
What I did was built a power adaptor board where I can cold boot the Arduino, and in the setup() I can enable a pin to turn on the Parola power (after which I delay 1 second to let the chips fall where they may). Hence, when I power up the Arduino, if there are any artifacts on the displays, a warm reset will clear them every time.
The power adaptor uses a 2N3904 to drive a P-Channel MOSFET. It's not designed for high speed switching on and off but it works on my 20 modules every time. Sort of a digital "magic wipe"...
In my project I'm only using 10 of the modules (it's a birthday present for my brother). There's a DS3231 RTC, a Bluetooth HC-04 (connected to Serial1). The project is controlled by any Bluetooth terminal so I can toggle between clock and scrolling message, any changes are stored in EEPROM for a reboot. On the inside from left to right you can see my power board, MEGA with proto-shield; RTC and Bluetooth, and buck converter to take 9-12VDC and knock it down to 7V to feed the Arduino's power jack.