what are some of the issues involving trade that have tarnished China's image in recent years?
In addition to the above answer, which covers it pretty well, China's image in the business world has been hurt by the extensive dumping of goods onto world markets at below cost prices, forcing prices for those goods down overall and undercutting what domestic manufacturers and growers can charge for their products. This forces many of them out of business.
This is especially true in agriculture, where the Chinese have been dumping apples, apple juice concentrate, and pears (to name a few) and other fruit products. But their dumping efforts have also included everything from off-road vehicle tires to solar panels to cigarette lighters. It is part of a long term effort on their part to capture a bigger share of world trade markets by eliminating some competitors altogether, using what many consider to be unfair and unethical business and labor practices.
A lot of what is bothering Americans about China is simply that they produce things less expensively than our companies do. But there are also a couple of more legitimate issues that have tarnished China's image.
First, there is the issue of intellectual property. China's government does very little to try to prevent pirating of software, films and music. They do not really try to prevent the manufacture of faked goods -- ones that pretend to be brand name goods but aren't.
Second is the issue of exchange rates. Other countries believe that China has been artificially forcing down the value of their money so that they will be able to export more easily to other countries.