Well, I read a blog in a pretty serious Norwegian newspaper. It was written by a Norwegian journalist, Sven Egil Omdal who's stationed in Brussel. Unfortunately, it's in Norwegian, so I can't provide a helpful link.
What it's all centered around is that when the new constitution becomes effective next year, the ruling party, Fidesz, will control the legal system, the central bank and the media.
Changes to the way elections are done, and a reduction of parliament from 386 to 200 representatives makes it practically impossible for new parties to gain seats. There is more, and worse, but that's the general gist of it.
I do not know the anything about the validity of these claims, and I am inclined to doubt them since I haven't found any other articles about it. I found some about criticism of the constitution based on considerations of discrimination.
But I haven't looked everywhere.