Absolutely no problems whatsoever. Passports generally do get stamped, but China doesn't care whether you've visited Taiwan or not. China is happy to welcome US citizens. The immigration officers never smile for some reason, but they are pleasant, efficient and polite. When you clear immigration, there's a little "voting box" where you can "rate" the officer, "good experience," "bad experience," something like that. If you press the "good" button, you'll receive a nice "thank you."

China is not an evil empire, and the only contact you'll have with the government is getting your visa, and clearing customs and immigration, which is faster, easier and more pleasant than in the U.S. Once you're there, you can go anywhere you want (except obvious off-limits places like military installations), photograph whatever you want, and say whatever you want. What is important in China is not disrupting the social order -- as long as you don't try to organize political demonstrations, or prayer meetings in the middle of Tian Anmen Square, or otherwise cause trouble, you can do whatever you want, no one will try to keep tabs on you, or any of the other popular misconceptions of those who have never been to China. China's a wonderful place to visit. Have a great time!