As hard as it is to blow an alumni interview, I have seen people do it, and heard some very shocking stories. Here are the things that you definitely should not do at an alumni interview.
Do not tell an alumni interviewer that you are applying to the school because a parent made you.
That is going to lead to a rejection letter (then again, you might want a rejection in that case).
Do not wear or carry paraphernalia from another university.
We really do not care where your sibling/parent/relative went to school; we want to know that you are focused on our alma mater. Showing paraphernalia from another school suggests that your attention is divided. It does not matter whether or not that is actually the case, because it is what we will think is the case.
Do not ask ridiculous questions.
You may have been taught that the only stupid question is the one you do not ask. But, asking the question of the wrong person is does not make you look smart. If your interviewer graduated 20 years ago, asking what the dining hall food is like will not demonstrate that you are much of a thinker. Same goes for asking about a specific club that clearly could not have been there 20 years ago (e.g., Wii Gaming Society). Your interviewer is generally up to date on the basic university statistics, and can tell you a great deal about the character of the university, the rigor of the coursework, how approachable professors tend to be, and the culture of the university. Tailor your questions to things that the interviewer is likely to know, and if you do want the answer to a question that the interviewer is not likely to know, phrase it as: “Do you know who at [Your University] can tell me about _______?” Again, this is an alumnus, not a current student.
Do not confuse being interesting with being a braggart.
We want to know what is interesting about you, not how good you are. Let your accomplishments speak for you instead of speaking for yourself. As an example, telling your interviewer that you can run a mile in 4:31 is not nearly as impressive as talking about your passion for running and possibly dropping a quick sentence about how your dedication paid off in a 4:31 mile time. Remember that your accomplishments are in your application and it is your character that interests us.
Do not start ranting.
Be very careful not to start ranting about the state of the world without linking it to your goals, passions, or activities. For example, one student I interviewed [details changed for privacy] was passionate about fighting hunger. It was interesting to hear about the canned food drives she organized, the awareness she raised, et cetera. But then, she starting going on and on about how Americans do not care about hunger and how apathetic we all are. As someone who used to volunteer in a soup kitchen, I did not appreciate her remarks. Even if I never lifted a finger for the hungry, I would not have been impressed with the diatribe, since I know a number of people who care very much and actively work hard to fight hunger.