John, I think that the Mccanns are behaving very well. SY are in charge now and they are keeping out of the way.
They did their initial search in a different way to some. Having physically exhausted all the sensible places to look in the vicinity, they thought in an 'encompassing everything' sort of way. They listened to advice and acted accordingly ... posters, letters, appeals. later the media involvement, publicity, kept themselves physically fit, and mentally supported by the church. When it became obvious that people wanted to send money in, they set up the search fund, formed a committee and the HTFM group of volunteers.
Then they took advice and employed Metodo, followed unhappily by a fraudster and finally the two PI's. They constantly found new ways to publicise Madeleines disappearance. These things dont happen without a huge amount of thought, dedication and effort.
They did all this whilst dragged down by sorrow, whilst being stalked and hounded by Bennett and his cohorts ... and with Kate at obviously near, or actually in, breakdown.

Right from the start they had a stalwart group of people backing them

, but think of the way they must have been dragged down / destroyed by a vociferous mass of people, many jealous low-lives, who could see no good in them and continually criticized them; tried to destroy them.
Even called them murderers, of their own daughter.... and even insinuated that Gerry had an unhealthy relationship with Madeleine, so had to kill her before she started school and blurted it all out

.
I could go on ... but I will leave it there.
They were magnificent. I suspect that Gerry was the driving force
These things dont happen without a load of work. Yes, they made some mistakes, but they searched alright. Their search was in a more planned and a more advanced way than many of us would have been capable of.