Although the memorial itself is not at the center of such conflicts, the Nanjing Massacre is a source of tension and controversy- especially between China and Japan. One reason the Memorial Hall was created was due to the trend in the 1980s of Japanese politicians and writers attempting to alter Japanese historical textbooks and write the Massacre off as a minor incident; The Chinese government wanted to remind its people and the rest of the world of the event, and that such happenings would not be tolerated.
Visitors to the Memorial Hall often remark that the mood of the Hall is very somber and silent. One such experience is referenced here in a blog-post by a traveller who visited the Memorial Hall. The poster also subtly (and perhaps unconsciously) argues that the previous attempts by Japanese politicians to play down the event were bad (for lack of a better-fitting term), and agrees with the Chinese government's reasons for creating the memorial.
Recently, the Japanese government has begun to offer compensation to those who were directly affected by the Nanjing Massacre. One woman (80 years old) named Xia Shuqin won 4.55 million Yen from the Japanese government in compensation (read about her story and the rest of this story here).
Also recently, a Chinese director named Lu Chuan has started to create a film called The City of Life and Death (also known as Nanjing! Nanjing!) that will document the Massacre from many different historical perspectives (with both fictional and non-fictional characters) and attempt to further explain the struggle of the those living in the city during the Massacre. (Somewhat Off-topic: I found this quote from the article quite amusing:
" The director believes there are three ways to solve China-Japanese relationship problems.
'First, we destroy Japan. Second, Japan destroys us,' he says. 'Or the third way is we try really hard to understand each other.'
'I think we should choose the third way.' "