Do not criticize the food: Peruvians are very, very proud of their cuisine, especially ceviche. Many will tell you that it's the best in the world. Others will rave about Gaston Acurio, a famous Peruvian chef (never heard of him? Do some research before you go). Don't compare Peruvian food to other foods and always make compliments about how good things are.
Don't tip: Having spent so many years outside of countries that tip I totally agree with not tipping. It's kind of an insult in Peru. Sure you may give the taxi driver your change, but you'd probably never tip. It's like saying the business owner doesn't pay their staff enough money, or it could be seen as a bribe. When in doubt, do what others do.
Be careful about gestures: The ok sign can mean OK, fuck off, money, or even gay depending on the situation and where you hold your hand. The pursed hands which in Italy would mean delicious in Peru mean pfft, really? The thumbs up and the peace sign (when done with your palm facing you) can mean fuck off. There are a lot of interesting videos on Youtube about gestures around the world that are worth taking a look at.
Forget about being on time: Peruvians are very laid-back and time is no exception. Don't show up on time. If someone invites you to dinner at 7pm, they probably won't even start cooking until 7pm. Half an hour late is the norm. It can be frustrating when you're supposed to meet someone. If someone is ten minutes late they're on time, so take that into consideration.
Don't be aloof and unhappy: Peruvians really enjoy life. They always seem to be happy and smiling even when times are tough. Follow their lead and focus on the positive, rather than the negative.
Don't disagree when Peruvians say they are Americans: I tend to break this rule. Some Peruvians will insist that they're are Americans because they live on the American continent. The word for American in Spanish is norteamericano/a.
Don't be afraid to touch people: Peruvians usually give an air kiss when they meet friends and men will embrace and pat each other on the back. Touching goes along with a small personal space bubble.
Don't say Pisco is Chilean: I pity the fool who says this. Pisco is Peru's national drink and they're extremely proud of the fact; even those who drink Chilean wine.
Be careful about what you say about Spaniards: They conquered the Incas in the 16th century. According to Peruvians, the Incas were smart and strong warriors. Many Peruvians are still bitter about the Spaniards being the cause of the end of the Incan Empire.
Don't Stereotype: Yes there is running water and electricity in Peru. Not everyone looks like the Peruvians you'll find in National Geographics. There are blond hair, blue eyed Peruvians and there are filthy rich Peruvians. Open your eyes and ears and shut your mouth. You may just learn something.
Don't be ignorant: Do a bit of research about the history, culture, and geography of Peru before you go. There's no excuse for not knowing a bit of the basics.
Not adapting: When in Rome do as the Romans do. Adapting to the local culture and customs will go a long way.
Don't act superior: Your country might be different but that doesn't necessarily mean it's better. You can learn something from everyone.