I'm Hungarian, I've been following our football for a long time.
The biggest problem is the players mentality, when any young player gets one match in the first division, he thinks he is a star, and basically, stops working hard enough. There are countless of examples.
That basically brings us to our coaches: There haven't been one Hungarian coach at any more or less respectable foreign club for I don't know how many years, lets say 10-15. Of course here I'm not counting László Bölöni, since he played, and educated himself in Roumania). Unfortunately these coaches think of themself really highly, every year there are coaches saying: I could train Barcelona, or any other team. It's *bleep* crazy, they actually mean what they say.
Now I'm going to write a really clear example: Ádám Szalai is our highest rated player, he signed for Schalke last summer for 8 million €. After our quite good qualifying campaign last year (won against Turkey, played really good overall), he goes out saying that nobody can expect this national team to have a real shot on qualifying, when our average player is on the Championship level, where as Turkey, Roumania, Holland players are we know where. There are not one single qualified Hungarian coach, we need a foreigner. He goes on saying that his advice to every young Hungarian player is to go and develop at a foreign club. It's worth noting that Szalai played abroad since he was 16. The response to this, is that he doesn't get invited to the national team with the new Hungarian coach any more.
Our football can't take any critisism, when a coach in our league looses a game, 9 times out of 10 these are the reasons: It was to hot, the pitch was bad, the referee made mistakes against us, we were tired, we have to many matches this month. This summer, our riches team Videoton got beaten by a side from Montenegro in the CL qualifying.
Lets take the case of Dzsudzsák, when he was 21 he transferred to PSV, did really well. Lille agrees on a transfer fee with PSV, but he rejects the contract, saying he doesn't want to play in the French league (I think Lille were champions that year, not sure). He transfers to Anji Mahackala, and half a year later to Dynamo Moscow, where he is now as well. That's the player our young people have to look at.
International football, doesn't want to sign a Hungarian player, even if equally good, they rather sign Slovakian, Roumanian, Serbian ect, becase of the mental issues. A player agent said this. From the countries around us the players, fight until they die, unfortunately we don't have that mentality.
I lived a lot in Sweden, the technical capabilities of the players are equal, but the difference between a game there and a game here is astonoshing. Here in Hungary, every team play for the result, which means a lot of defense, and lots of goals from free kicks, corners. In Sweden every player is encouriged to dribble, to do those one on ones. My favourite team here (Diósgyőr) had a coach who forbid his players to dribble. I mean he said it live, it was "official". You can't develop.
Last point: In the youth until 15-16 Hungarian players are at the top. Why? Because they have extraordinary hard physical training, running, lifting weights, ect. Real Madrid youth team was here a month ago, and they beat the best Hungarian team by 1-0. The difference is, that foreign players are trained with technical stuff as well, we Hungarians can make up for that with good physic, but they will have the advantage when they grow up, and are 20. This is the BIGGEST problem. We only care about results, even when the kid is 12 years old.
So yeah these are the issues, doesn't look like there will be any change anytime soon.