This is heavy nerd, feel free to skip.
When I was working on Ed's guitar yesterday, I took some time to reacquiant myself with the whimpering horror of the Floyd Rose Double Locking Tremolo.
This beast was invented in the mid-1970s by a chap called Floyd Rose (bet you didn't see that one coming). He came up with it because he wanted a tremolo that you could go Jimi Hendrix-style mental with, without pulling your guitar badly out of tune. In that regard, he succeeded—when properly set-up you can do just about anything with a Floyd Rose and it won't have any serious effect on the tuning. That, in my view, is about the only way in which he succeeded.
The Floyd Rose is a wildly impractical piece of technology. In order to restring a guitar with a Floyd Rose you have to first chop the ball-ends off the strings, then clamp them into the saddles at the bridge (to do this properly you must turn the set screws so hard that you will inevitably strip quite a few allen keys over the years). Once they're all in you have to spend ages tuning the strings, letting the bridge adjust—which pulls them back out of tune again—then tuning them again. It typically takes a day or two before you actually have a guitar that is both in tune and has a balanced tremolo. If you're switching between string gauges or brands of strings it can take even longer. Once this is done, you have to clamp the strings in place at the nut, making large adjustments to tuning a fiddly and laborious process.
If you you try and change the tuning of an individual string (say switching to Drop-D tuning) then this will lower the overall tension on the tremolo, pulling all of the strings out of tune. Similarly, if you break a string, the increased tension on the other strings pulls them all out of tune, and sometimes causes more to break. The second fact makes it foolish to gig with a Floyd Rose equipped guitar unless you have at least one backup.
Ed has made several modifications to his Floyd Rose over the years (including adding extra springs and placing a block of wood under the rear of the tremolo) which essentially make it into a single-action tremolo, like the Wilkinson Tremolo on a Strat. This makes it less versatile as a tremolo unit, but makes it much, much easier to use.
Even so, the actual tremolo unit is a pretty shocking piece of design. The set screws that allow you to adjust the intonation are positioned underneath the strings, so you have to remove the strings in order to make any adjustments the intonation. You cannot raise or lower the saddles individually, which means that you can only adjust the action by tightening or loosening the bolts that anchor the unit in place. Also, the clamps that hold the strings into the bridge are positioned at a 90º angle to the string pull, which makes the strings more likely to break at that point.
All told, a guitar with a Floyd Rose Tremolo is like an old Rolls Royce where the driver's seat is not covered by the roof. It's a design feature that assumes you have staff to do everything for you, as it would be really unpleasant to do it yourself.