let see if you like this my first try
1) You are using pins 0 & 1, this will interfere with the serial communications.
2) You don't use multiplexers like that. What is the multiplexer part number anyway?
3) You don't connect switches to the analogue pins.
4) You should do a proper schematic where we can see what the switch connections actually are. What you have is a construction diagram, you draw that after you draw the schematic.
5) What is the part number of your driver?
6) The arduino pins can't source enough current to drive the common anodes of the display. There are 7 segments and a 30mA limit (don't design for 40mA maximum) so that only gives you 4mA per segment, this will not be bright enough.
7) You need current limiting resistors in the cathodes.
Sorry but it doesn't even begin.
Try looking up how to drive seven segment displays in the playgroundhttp://www.arduino.cc/playground/Main/InterfacingWithHardware