1. Never re-gift in the presence of those who gave you the gift.
2. Chinese gift exchanges are good ways to re-gift, but if you are going to do that, make sure you follow rule number 1, especially if the gift was unique enough that the person you got it from will immediately recognize it.
3. Always check the package throughly, especially if it's something where it's not sealed or if the seal could be broken without anyone realizing it...the teapot mentioned is a prime example of why this is important. Purses, wallets, bags and other storage products are also important items to check.
4. Make sure to clean all dust and cobwebs off the gift.