This is to do with the ukc website, I hope this is the right place for this.
For example, hovering over Crow's Nest Wood Quarry on the map, the pop-up says there are 30 routes, but on the crag listing page I only see 3. Similarly the map advertises 3 routes on Cut-thorn Crag, but on the page I only see 1. Is this a bug, or are there more routes hiding somewhere that I'm missing?
These two numbers are not linked despite the fact it looks like they should be. The reason is that, when the database was set up, it consisted mostly of crag listings only. The routes were added by various users and from Rockfax sources over time. For minor crags, they simply not have had their routes uploaded yet.
So in your example, the crag Crow's Nest Wood Quarry has around 30 routes as an approximation, but only three have been uploaded as fully entries to the route listings.