Racist vs. Outdated vs. Confused

December was a pretty fun month. I made friends and got to see my family for the holidays. But my friends and family said some things that I must address. In class, we've discussed racism before and tried to express ourselves in a way that is as inoffensive as possible. But after talking with friends and family last month, I have come to the conclusion that you cannot avoid saying something offensive forever. However, this doesn't make you racist or a terrible person depending on how you say it.
From my experience, an offensive statement can be put into three broad categories: confused, outdated, or racist.
Confused statements are made purely out of a lack of information and don't tend to severely offend anyone. Last month, I was talking with some classmates and brought up the fact that I was adopted. One of my classmates was shocked and asked, "You're adopted? Why didn't you tell me?" I simply don't feel like reminding everyone that I was adopted. End of story. The boy's statement isn't discriminatory against adopted people. He was just surprised that I was adopted. One would have to be extremely sensitive to get upset at this.
Old people are an excellent source for outdated statements. When I play piano for my grandmother, she often requests an 'Oriental song' because she likes traditional Chinese music. Here's where things get dangerous. New York banned the use of the word 'oriental' in 2009 in state documents. Oriental is a term used to describe countries of Asia, especially the far East and was a term my grandmother has always used. It doesn't have a negative connotation like other racial terms, and my grandmother never intended to use 'oriental' to racially demean anyone. She grew up very close to Chinatown and often went there for lunch after work with her friends. And because 'oriental' has never been used as a way to look down upon a different culture, this term is more outdated than racist, although it can take a negative meaning.
My grandmother can be racist, though. Despite being Polish herself, she's referred to fellow Polish people as 'DPs'. I can only assume this is an abbreviation of the term 'dumb Polack', a very offensive, degrading term for Polish people. This is clearly a racist statement. As a Polish American who lived in a Polish-American community for most of her life, my grandmother is aware that 'polack' is a racial slur against her own race. My mother (third generation Polish American) has pointed this out to her several times. My grandmother is aware that this is an offensive term and continues to use it with the intent to offend someone. And that's downright racist.

But does that mean that you're only racist if you mean to be? Miley Cyrus offended many sensibilities with a 'funny face' picture that resembled a common Asian pose but repeatedly denied trying to offend anyone. Her defense was that she "was simply making a goofy face. When did that become newsworthy? It seems someone is trying to make something out of nothing to me," but really, Miley? Squinty eyes and a peace sign and you try to brush it off as a 'goofy face'? My jimmies have been rustled. 

What does everyone (no one) think about this? What counts as racist? And if you can define racism, what should be done?