The advantages of multiplexing are:
1. less component count.
2. smaller PCB size especially when you buy LED blocks arranged as 7 x 5 leds.
Disadvantages:
1. More complex to program when moving text or graphics.
2. Poor quality visual output.
3. More EMI generated because of switching.
4. Almost impossible for outdoor use because brightness would be low due to multiplexing. you need to have very high current to increase the brightness which will shorten the LED life and increase its cost.
Non multiplexed LED displays are far more superior for they use dedicated constant current driver chips with 16 bit shift registers, output latches and output enable pins making programming complex moving text and graphics a breeze.
I summarized the information about LED panel design in this link
http://www.8052.com/forum/read.phtml?id=154275
Mahmood