A problem that has definitely tarnished China's image (for those who know about the matter) is the number of Chinese workers who are literally (not just figuratively) killing themselves because of harsh working conditions. A particularly lenghy article on this phenomenon can be found at the link below, but other discussions of the problem can also be found through a google search.
The biggest problem with China is that it has a reputation for poorly built and dangerous products. The joke is that anything made in China is low-quality. The furniture and clothing falls apart. The toothpaste has antifreeze in it. You get the idea. The other image we have is of human rights violations and poor factory conditions. We still buy things from China because they're cheap, but we don't feel good about it.
Explicitly related to trade is the way in which China forced Google to allow the state to maintain control over websites and access rather than allowing its population freedom of information. It is clear that this is linked to China's desire to maintain control of knowledge and its economy. However, this is also related unfortunately to its abuse of human rights.
One of the major issues that has tarnished China's image (in addition to those already mentioned) is the issue of China's unwillingness to let its economy truly open to the outside. China thrives on exports, but tends to set up barriers that make it difficult for foreign countries to access its market. It also manipulates its currency to make sure that it stays weak and does not endanger China's ability to export.
Ironically enough, China is in the news just today as officials investigate several Apple stores in a town called Kunming which appear to be fakes. One store owner being investigated says that while his storefront itself is illegal, the products he is selling are legitimately Apple. Overall, China is one of the fastest, if not the fastest, growing economies in the world, but things are not all flowers and wine. College graduates have had a difficult time finding jobs in recent years, and of course, human rights abuses and/or working conditions in the sweatshops are frequently a point of contention with the United States.