LED and resistor question

Just about an hour ago, I was testing a board fresh off the assembly line. It had a reversed R-Pack, which creates a similar situation... A shared current path (6 LEDs in this case). I noticed that LEDs got dimmer when more LEDs came-on, and a blinking LED made another LED "blink" bright and dim. I've seen this before, and I know right-away what the problem was...