With fishing magazines and TV shows touting fluorocarbon over monofilament leaders, I have found that there are a lot of myths out there surrounding Fluorocarbon and the use of it for leaders.
First, fluorocarbon is not invisible in the water. Fact is that fluoro has the same refractive capability as water, so rather than a line attached to a hook which may shine and reflect light under water, which monofilament does, fluoro underwater is a dull line. The fish can still see it, but not as well which can prevent spooking skiddish fish. A helpful thing to remember is once flouro is nicked or has some abrasion to the surface the leader is much more visible to the fish. After casting a lot or fighting a fish, I check the line for damage. If there is no wear, no problem, otherwise I will cut the leader above the damage and retie.
Next, because flouro is denser than water, it actually sinks. This can be good, bad or indifferent depending on how you are fishing but something which should be considered as well when you are working a lure. Lures and flies like poppers, gurglers and suspending baits can be effected in a way where they do not work as well or as a benefit because rather than skidding across the top of the water or staying in a specific water column the line, when pulled, pulls the lure down then the buoyancy of the lure pulls it back up (this is especially effective on fishing a floating sand eel fly pattern at night).
Lastly, due to the density of flouro, the ability for the line to knot is compromised. Where monofilament is slightly softer, mono knots typically dig into the material and hold much better than flouro (where a knot is much more likely to slide). While an improved surgeons knot and blood knot will work fine for most applications, once you begin using flouro over 30lbs, you will need to begin attaching this to your main line with slim beauties and huffnagel knots. For the leader to the hook or barrel swivel, improved surgeons knots will work, but if you are looking for a strong and easy to tie loop knot, I prefer the Homer Rhodes for line over 30 and the non-slip mono loop for thinner diameter lines. I have attached some links below to help with the knots outlined above.
Slim Beauty (my preferred tarpon leader knot)
http://www.midcurrent.com/articles/knots/slim_beauty.aspx
Bimini Twist to Huffnagel Knot (common offshore knot)
http://www.midcurrent.com/video/clips/anderson_bimini.aspx
Homer Rhodes / Non Slip Mono Loop Knot
http://floridasportfishing.com/magazine/the-rigging-station/the-tightest-knot-isn-t-always-the-best.html