I have never been to Edinburgh, but mm/year isn't the best way of saying if a place is wet or not. A city that has that horrible misty rain two thirds of the year may not score high a mm/year measure, but in reality you'll be wet two days out of three.
I've noticed it rains differently on the continent. When it's raining here people will often shelter in doorways or bus shelters because they know it'll usually be done in a few minutes and they can wait it out. Scottish rain is very much a "today it is raining, and that's just how it's gonna be" thing. If I'm honest it never bothered me that much - a brolly will suffice in the city or a waterproof on a walk in the countryside.
Yeah, I don't know how Edinburgh is specifically, just that in general I think using this measurement is hiding part of the truth. In places with wet and dry seasons, you might get rain for a month and the rest of the year is dry, but mm/year might still be very high.
The wikipedia article Arethuza posted shows average precipitation for European cities by month as well, so you can actually see how this breaks down. For example Istanbul definitely has this - it has more rain than Edinburgh overall but it's concentrated in the winter months. Interestingly (and as a total aside) I was there in February once and was shocked when the temperature was below zero, it was a relief when we escaped to Izmir and it was >15C :D
