What is the advantage(s) of multi-rotor configurations (besides being a lot a fun) as opposed to the single rotor (traditional heli) style??

Easier to fly, and can haul more weight.

not too complex as a heli , and also scratchbuild-able

Simple.
Easier to build.
Easier to fix.
Cheaper to fix after a crash.
Tougher. Most of the time less things break/bend compared a heli.
Easier to fly.
The flight controllers can do amazing things.. GPS hold, Return to home, Carefree, Autoland, Waypoint mission flights...
Etc.....

So far, all the reasons given (except for the one that says that they can haul more weight - which is incorrect) make multi-rotors a really fun toy for hobbyists to play with. Let me rephrase the question. Are there any advantages of multi-rotors over conventional single-rotor configurations for real-world, commercial/military applications?

Wrong forum, we are hobbyists

I can haul an all up weight between 12.5 and 13kg for around 6 minutes with a 1355.6mm span (1m span octo running 14" props).That's fairly efficient. Many professional AP fliers have gone from single rotor to multirotor and say they would never go back.

Mark

Firstly - I am a part-time commercial AP photographer and have been for 5 years.

I have sold my Trex-600 cameraship and do all my commercial aerial photo work by multicopter now. The customers see it as a smaller risk. I thought they were being soft until (after a 9 month heli break) I started up my Trex-700 camera ship on my back yard. While it was spooling up, I found myself stepping back being cautious. If I felt like that, it is no wonder some of the customers find helis intimidating!

Advantages of a multi over a heli:
# I can comfortably fly a multi in a more confined area than a heli - including a photo and video shoot inside a working galvanizing factory.
# Smaller moving chopping parts.
# Easier and quicker to repair than a heli. The basic build is a similar cost.
# More stable - I am able to solo shoot with a mono-lcd eyewear (eyetops).

Advantage of a heli:
# Orientation. I could fly my T600 to 800' and know which way it was pointing. I could fly it 250 yards away and know which way it was. The multi - even with lights is symmetrical over 300' or 100 yards away.

I still have the 700 but I don't know when I will use it. For the really big jobs where I need to go over 400', I factor in the hire of a C172 aircraft (as I did today). I did 3 jobs during one hire. Know your limits - a risky job isn't worth a heli or multi...

Just my 2c worth!

Pete

rmteo is correct, physics prove that multirotors does not scale efficiently.
A tricopter can theoretically fly more than your setup, but needs bigger props and motors of course.
Your main gain is redundancy, you can afford and arm failure, maybe even two.