PCBs are costly and take time. Complex ones even more so. Even the best PCB designers make mistakes. Prototyping is the building and testing of any circuit before the point where the designer considers the design finished and tested.
You may wish to build up a small prototype circuit on stripboard of the analogue signal processing/amplifying circuitry in the design, or of this custom digital multiplexor, before making a proper PCB.
Try and use development kits wherever possible.
If using stripboard, perfboard, or any other type of pre-made, drilled, copper-tracked PCB for building prototype circuits on, it can be useful to sketch out the component placement and electrical connections before committing to soldering.
A great tool for sketching this out is a printed out paper design which reflects the PCB layout. http://incompetech.com/graphpaper/ has some great grid generators that you can print out.