In Zusak's The Book Thief, what mistake allows Death to be severely disappointed in himself?

Mistakes, mistakes, it's all I seem capable of at times (23).

Death makes this observation about himself in the section entitled "Arrival on Himmel Street." He tells the reader about what happened after Liesel's brother, Werner, died. First, Liesel wakes up and catches Death at the exact moment that he extracts Werner's soul from his body. This is part of the reason Liesel captures Death's attention. Death also tells the reader that he sometimes becomes distracted because he never gets a vacation. As a result, distractions tend to be a way for him to take brief vacations from time to time. In this case, however, Death becomes more invested in Liesel's life than he should have permitted himself to be. For example, two days after discovering Liesel, Death says the following:

Several times, I warned myself that I should keep a good distance from the burial of Liesel Meminger's brother. I did not heed my advice (23).

Distracted and curious at the same time, Death visits Liesel on the day her brother is buried in an icy, shallow grave. He is caught up in the plight of this little girl, which captures his interest in Liesel's continued story. He becomes invested in watching her life play out because he marvels at her strength and fortitude. Not only that, but he witnesses her steal her first book before she is dragged away from her brother's grave and he wants to know what a little girl will do with a book called The Grave Digger's Handbook. 
The fact that Death allows himself to become consciously invested in Liesel's life is his mistake. Death's job is to be objective and unattached. Even though he doesn't play favorites by allowing Liesel to live longer than her allotted time, he shouldn't care about anyone in particular because it makes his job more difficult. It also leads him to the following discomfort: "I am haunted by humans" (550).