I've visited many of the places the Via Dinarica touches during many travels down there by hitchhiking, motorbike or car.
Many a time I made myself the promise, once I'm retired to hike right out of my front door all the way down into Greece - which would include the Via Dinarica (which didn't have this name back then).
The idea to define it a long distance trail is just great.
There is so much great landscape (karst it is, giving it a very unique appearence).

The people are, hmmm, special. You could call them grumpy. Not the overwhelming sweet smile (in order to get your money smart) that follows well developed and educated tourism locations.
Its more of a straight habit the people in the interior of the country have.
I personally like the people down there.
Would be afraid a little bit about landmines though, the wars ended in different places only 25-15 years back. Not sure if they cleaned out everything perfectly.
The further down south the more exotic and maybe scary everything becomes.

Be prepared that English knowledge is almost non existent among the locals. Only young people might speak some.
German is more common, due to many locals having worked for years in Germany. Italian is also somewhat common, especially among the old people. 
For food, meat is the most common you will get. Cheap and good. Would be hard to get through if you are a vegetarien. Alcohol is common and cheap. Be prepared to receive many a welcome drink.
Resupply might be limited in many places. Hiking gear in good quality might be impossible to get. Postal service might be doubtful. Cell coverage poor. Mountain rescue is non existent in most places.
There is no such thing as "hiking culture" in those countries, you might have difficulties to explain to locals your idea of hiking the whole way. Walking is common, but only for the poor. Getting up summits is done by car (and those summits are flooded on weekends).

Navigation on both trails might be difficult at times. There will be no such "all the same the whole length" trail thread like on the AT, its more a concatenation of existing trails of various origin and quality. There will not be a unique blazing, but just the signs of the local paths (which can be everything from a colored blaze to a aluminium plate with numbers, names and distances) and some Via Dinarica signs here and there.
There is no guide book as far as I know, you have to resort to the online resource linked above.

If you want to extend the hike by starting north of the Alps you are welcome to be hosted in my place <G> (maybe we can do some part together)

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Just a quick word regarding the different countries:
While Slovenia is "like Austria, just a different language", and Croatia widely is a touristic country (very clean and pretty expensive), the more exotic part starts with Bosnia, roughly half of the inhabitants being Muslim, and propably you will see many relicts of the war.
Montenegro has highly motivated started off after the war as a very hopeful project, but soon suffered a lot from corruption and other problems.
Albania is a totally different story, having been locked away from the rest of the world for many decades and now it seems to be, together with the bordering northern neighbors, a Mafia hotspot.

Some more words about the food down there.
Its all barbecue. Every Gostilna has a huge grill outside which they light up late in the AM and put a pig on the spit. The turning mechanism for the spit usually testifies of great phantasy, you may see every possible mechanism that can turn a spit - waterwheel, windmill, car gearboxes, elevator chains, scrap pieces of motorcycles and others.
In the muslim part of the countries they will put mutton on the spit, but otherwise the same procedure.
A huge plume indicates for many a km that the grill is working, and sends unresistable signal to your mouth watering and belly grumbling.
You walk up, ask if the meat is ready and sit down, in a hungry-lion mood.
You will mostly get bread as a side dish. You may get vegetables, but this will also come from the grill. You wash it down with a beer or two and a brandy for to diagest the meat.
Don't ask me if the food is healthy, but its all local, its irresistable, its good and not too expensive. And many a times its the only option. 

People:
People in all the southern countries have a strange habit that everybody does the same at the same time.
So, seeing many cars in front of a gostilna should not shy you away, but encourage you to just enter, it usually means that this one is the best gostilna in the vicinity. You should not expect too much by entering an empty gostilna, there might be a reason (a negative one) why its empty.

Southern people are loud. It may happen that a silent backpacker in the gostilna gets lost in respect of service. You may have to be loud as well to get attention, even if its not easy for somebody coming straight out of the quiet forests.
People know what the horn of the car is good for, and they make heavy use of it. Walking alongside of the road you will get honked on by every single car. Nothing evil-meaning, just their way of communication.

Souther people are hospitable, especially families are. It might happen you sit at a parking lot bench unpacking your meager lunch, the family on the next bench might hand you over a bunch of grapes or a melon. The mother of the other family feels responsible for you. They are not deeply interested in who you are and what you are doing (they might not get the idea of it anyway), its just their age-old tradition. 

People in the south are infamous for littering. Parking lots and picknick areas litterally are litter places. Even if there are outhouses most people prefer to pee and **** in the nature. Wherever a car can stop along any road you have this cordon-ring of toilet around.

People in some of the southern countries think bad about Americans (I'm sorry for that), first they had lived in a communistic state for decades when every day they got indoctrinated how good is communism and how bad is capitalism, and then there was the war when NATO ended up bombing. Don't take it personal, and provide by not showing off with your nationality.

Wildlife:
There is not much real wildlife, all southern countries are (legal and illegal) heavily hunted and had been so since ever, so almost every edible animal is rare.

You will see evidence of boars. You will not meet them in person (hopefully not), just be careful. Its not a big kind of boars, but they can be aggressive, especially if its a sow with youngsters.

Expect to meet many stray dogs that live on the litter. They occupy some of the places you might like to stealth camp. You as a hiker are sometimes coming from behind (they've learned every enemy comes from the the front, the road) so they might be taken by surprise and make big fuzz. No danger from them, they will run as soon as you bend down to pick a stone. Walking sticks help, too.
There are shepards with big herds of sheep and goats, that have dogs to help. Don't mess with them, they mean serious business when they decide you to be an enemy.

There are a few bears somewhere in the mountains, feel very lucky if you find any evidence. There are snakes, some of them venomous, but none really treacherous or known for many casualties. There are bees, wasps and hornets, and of course moskitos. You will easily be able to deal with these. 

Places:
Some places that I know of, you must not miss:
- Postoina - karst caves (the one famous one, and many others around)
- Plitvice - lake district. Take a full day to discover the whole are.
- Velebit/Paklenica - outstanding beauty, also great for rock climbing
There are many other great places, the website does pretty well in giving a good impression. 

Have fun!

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Added June 26:  Just to add another pretty important detail:
Due to the war and ongoing fightings in the Middle East a flood of refugees washes up through southern Europe. The dense situation in Turkey doesn't exactly help.
They count up to millions of people of all kind, flowing this way and that way, hopelessly straying, stuck in numbers of tens and hundred thousands in desparate camps, never welcome and save in any place.
Police and military tries very hard to keep the three main groups apart, the normal local people in their normal habitat, the tourists in their tourism happyland, and the refugees out of sight of both the other groups.
Well, as a hiker going north to south you swim against the current, thus being less suspicious, but still it might happen that you are mistaken for refugees.

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