It reminds me of the old joke:

Passenger "Excuse me young man, do these planes crash often?"
Steward "No ma'am, only once..."

No, it's not common to have so many failures, but it's strange that all the components are switches. Are you using them within their ratings?

110ohm...  Isn't that kind of low, or is that normal now?  I've always used 10K.

It is correct in this context:

http://playground.arduino.cc/Main/DisablingAutoResetOnSerialConnection

Did you try what PaulS suggested? If so what was the output?

Just to echo what GM has said, get a pack of E12 series resistors (E12 meaning the range of values you get) and when you start to run out of a particular value, buy another 100.

If there's money involved you might try posting a request in the 'Gigs and Collaborations' section.

Get down to Maplin / Halfords / Screwfix and buy yourself a pack which contains an assortment of terminals and a basic crimping tool.

I would suggest that to start with you try getting the shift registers to work with some ordinary leds before tackling the RGB problem.

To help with this you might want to consult Nick Gammon's excellent write up http://www.gammon.com.au/forum/?id=11518. Wire it up, play around with the values you shift out and see what happens. And try to think in binary!

A check box to confirm that they have read it, and a statement to the effect that any posts not conforming will be deleted? That way the mods have a bit of leeway!

Yes, it's as simple as that. From experience place a length of insulated wire lengthways under the chip so you don't have to struggle to remove it should you need to reprogram it later! If you are using an ic socket that is...

There's a similar thread running next door which might help!

http://arduino.cc/forum/index.php/topic,165084.0.html

You have up to seven segments lit at any one time so yes, you need one resistor per segment. Also keep an eye on the current draw. The typical '595 is only good for around 70mA, that's three segments simultaneously, so either use a transistor to control each segment or use a led driver chip (I can't remember the model number!)

The status is 'V'. From the comment in the code:

V - No sats and not a valid signal.

You need to wait until you get a status of 'A'.

What about the resistor on pin1 to hold reset high?

I still haven't seen any code that does compile.

Try Auto formatting your code (Tools -> Auto Format) and then see if anything stands out?