I added a 16V 1000uF electrolytic polarized capacitor to the power going into the LCD screen. Didn't change the flickering. It seems to flicker whenever it is refreshed. I played around with the code some and only have it refresh every 10 seconds. When it is just static there is no flickering. (also, the flickering seems to be coming from the LEDs that act as the backlight)
The only things I can think of that would be the cause of the flickering are: power or cheap LCD. :~ Could the Arduino not be able to deliver enough current to the screen when it refreshes? The datasheet says it typically draws 250mA. (doesn't give a min or max, just typical)
The other thing I noticed is that the time displayed on my 7 segment display is slow by about 1/2 to 3/4 of a second. (I compared it to a SkyScan atomic clock and an online clock) I don't need my clock to be crazy accurate, but 1/2 to 3/4 of a second is off too much. Could it be taking this long for the GPS to send the NEMA data to the Arduino, have the Arduino parse it out, then use it to set the time? Would the update go any faster if the GPS was hooked into the hardware serial pins 0 & 1 TX/RX?
I did a simple test and hooked up the PPS signal wire to a teeny tiny speaker and could hear the pulses every second. They matched exactly (as best my ears could tell) to the seconds from both of my clocks. So, I think a plan would be to have the Arduino listen to and count the pulses and use that to sync for the clock. Unless anyone has suggestions. I'm all ears. 