What will happen if I drive LEDs in parallel from a TLC5947?

Btw, if you're interested in the project I'm using these chips in, you can check that out here:
http://arduino.cc/forum/index.php/topic,139819.0.html

There are a couple minor issues with the LED modules I designed. I should have put a 10K resistor on them to pull down the enable pin so they don't flash when you apply power. And there is some kind of reflection issue in the data lines when I have more than six modules in series, where the LEDs on the last few modules will be messed up. It isn't a serious problem since six modules is a whole lot of LEDs, but I'd like to fix that eventually. I assume I need to put some resistors or caps on the data lines to solve that issue, though I haven't really had time to research possible solutions.