I want to include some latching DTDP relays... but oh dear

With the warning that I rarely make boards (and therefore you should wait and see if someone more qualified comments ) the layout looks OK to me. However there is something very wrong with the silkscreen output in the gerbers. The board outline is wrong and a bunch of the outlines are missing and all are in the wrong place. I'm not sure why because they display OK in Fritzing just not in gerbv (which means they are likely wrong, as the gerbers are what the board will be made from and gerbv is independent of Fritzing.) As well the connectors look odd, the pins are offset both in Fritzing and in the gerbers, looking at the Sparkfun part I believe the Fritzing part is wrong. This looks like an eagle to Fritzing bug where it offsets the connectors, they should be in a single row like a standard header not this offset vertical pattern. In addition an electrical issue: you need bypass capacitors, one .1uf ceramic and a 1uf to 10uf tantalum across the 5V power rails, as close to the power pins of the ICs as possible (I'd use a .1 ceramic on each ICs and the 10 uf tantalum near the 74hc595). The relays will cause inductive spikes when the coils energize / deenergize. The suppressor diodes in the 2803 will help but the bypass caps are still needed to make sure the spikes don't cause the 595 to clock when you don't want it to (and are always best practice anyway). There look to be some errors (non routed rats nest lines) in the breadboard view which may have a bearing on the missing silkscreen data or may not. In general it is best to start in one view (I usually use schematic) and make it complete and then follow the rats nest lines for the other two views. Trying to do connections in different views sometimes causes corruption in the parts database which may be what is happening here. (edit:) Cancel the comments above about the silkscreen, I obviously screwed something up as a reload gets correct silkscreen. So if you replace the connectors with the updated part below and add bypass caps you should be good to go for the pcb view unless someone else sees a problem. As noted you have some wiring errors in breadboard view.