Dussel wanted a book about Mussolini and Miep almost got arrested.

Mr. Dussel (real name Fritz Pfeffer) was not Anne’s favorite person when he joined the Annex.  They were in hiding, and it was already hard enough to be in such cramped quarters with so many mouths to feed without one more.  Also, Dussel had to share her room, which she did not enjoy.  So you can understand why Anne would often grumble about Dussel in her diary.

There is one instance, however, where Anne says specifically that Dussel put them in danger many times.  In this case, she gives a specific example and says it had to do with a book that he asked Miep for.  Remember that Miep was the one that helped them by bringing them things from the outside world.

Dussel has put us in danger for the umpteenth time. He actually had Miep bring him a book, an anti-Mussolini tirade, which has been banned. On the way here she was knocked down by an SS motorcycle. She lost her head and shouted "You brutes!" and went on her way. (Tuesday, August 10, 1943)

Miep’s quick thinking prevented her from being arrested.  If she had been arrested, that would have led to the Nazis finding the family in hiding because they would have questioned her.  This is why Anne says, “I don't dare think what would have happened if she'd been taken down to headquarters” (8-10-43).  Even though Miep would not have wanted to tell anyone, they would have interrogated her and possibly tortured her until they found out where she was hiding the Jews.  This is how Dussel put everyone in danger. 

Other, less serious examples of Dussel putting people in danger include his writing letters when he has been told not to.

Dussel is terribly lax when it comes to obeying the rules of the house. Not only does he write letters to his Charlotte, he's also carrying on a chatty correspondence with various other people. Margot, the Annex's Dutch teacher, has been correcting these letters for him. Father has forbidden him to keep up the practice and Margot has stopped correcting the letters, but I think it won't be long before he starts up again. (Friday, March 19, 1943)

Obviously, writing letters could be very dangerous.  No one can know where they are.  If Dussel is not careful in his correspondence, he could let something slip about his location.  This is why Mr. Frank forbids him from writing.  Why is it so difficult for Dussel to get along with everyone, and obey the rules?  He seems a little set in his ways, and not used to other people telling him what to do.  He also does not really seem to acknowledge the true danger of their situation.  He wanted to wait a few days before going into hiding, for example, and was surprised that the Franks did not get away.

Dussel's slips are an example of how dangerous the situation really was for the Frank family.  Having so many people in such a confined space can lead to many conflicts and nerves.  Yet Anne might have been right when she said that Dussel repeatedly put everyone in danger by not acknowledging the frailty of the situation and the reality of war.