What tips/advice would you give recent veterans in interviewing for a civilian position?

Getting to the interview is good news. My recommendations differ slightly depending on whether you're interviewing for a private or public sector position.

1. Preparation: Learn about the company (private) or organization (public) with which you will interview.
-Most companies have web sites that tell about the company and often about its leadership. Read all this stuff.
-Public sector organizations may or may not have web presence that helps understand the organization. If they do, read it. If they don't, look for the next organization higher up the food chain. For example, if you are interviewing for a job in a plans and strategy division of an Army major command, but can't find a web site for the division, look for the Command's web site and read all you can.
-Ping your network to learn about the company or organization in which you'll interview. There's a good chance somebody you know will know something about them. Listen objectively. Beware emotional praise or degradation.
-Review the resume you sent to the company or organization. Make sure you're ready to highlight any positive changes, such as completion of a degree or certification, during the interview. Conversely, be ready to respond to any adverse information they may have discovered through their own research. (If they have your SSN and birth date, they can do an in-depth background check, and credit check. Many private sector companies will do this before the interview.)
2. Dress: dress appropriately for the position you are applying for. If the company brags about their casual work environment and shows a picture of their CEO in shorts and flip-flops on the web, this is not an invitation for you to show up looking the same. Unless you are specifically instructed not to "dress up" for the interview, plan on wearing a coat and tie to the interview. If you are interviewing for a "dirty job," dress in clean work clothes. Ladies: dress like a lady.
3. Timeliness and courtesy. Pretend this is a meeting with your commanding officer. 10 minutes early is "on time." Treat everybody with courtesy and kindness. Sometimes interviewers and hiring managers will ask the receptionist or admin professional (a.k.a secretary) what they thought of the interviewee after he or she is gone. I did. Their opinion counts.
4. Answering questions:
-Answer honestly. If you don't know, say so. You might explain how you would resolve your temporary ignorance.
-Public sector interviewers, whether alone or a panel, will try to ask exactly the same questions to each candidate using exactly the same words and phrasing. Don't be surprised if the read the question to you.
-Private sector interviewers have a lot of latitude in what they ask. Don't be spooked if the interview goes shorter or longer than the time scheduled. It may have nothing to do with you and everything do to with the person asking the questions.
-Be prepared to support everything in your resume. Be able to tell more about every job and accomplishment. If it's been a while, brush up on the schools from which you received degrees.
-Beware of inappropriate questions. This doesn't happen often, but you need to be aware of the questions you don't have to respond to if you don't want to. You cannot be asked about anything through which the employer might discriminate against or for you. You can't be asked about health, age, sexual preference, marital status or kids, race, religion, or physical disability (except to the extent such disability may require special accommodation during the interview). There may be others, but those are the biggies. Good interviewers know how to get to the information they need without tripping into one of these restricted areas. If they do ask something stupid like what year did you graduate from high school, which can show your age, you can politely refuse to answer. "I'd rather not say. But if you need a copy of my transcript for some reason, I'll be glad to provide it to human resources.", for example.
5. Asking questions. Here's a chance to let the interviewer brag about the company or organization. Ask about their work, "What is most satisfying about your job?" Better yet if you've studied the web site and found a goodie, "What was the biggest challenge in getting the Command Strategic Plan approved on schedule?" Check on the benefits listed on the web page or in OPM. "Have you used the company tuition reimbursement program?" You could try something more personal, "Where were you working 5 years ago?" This one is very good if the interviewer has asked the ever-favorite, "Where do you see yourself being 5 years from now?" Make sure you know the next step in the hiring process and who should contact. Make sure you have the interviewer's business card or contact information.
6. After the interview: Thank everybody on the way out. Send a thank-you e-mail to each interviewer within 48 hours. Make notes about questions and environment for future reference.
7. Try to avoid phone interviews. Visual queues are very important to communication and they are eliminated in the phone interview. See if your interviewer has access to Skype or a video conference tool through which the interview could be conducted. If you have to do a phone interview, be sure to conduct your part in a quiet environment. No crying kids, barking dogs, etc. Always ask the interviewer to repeat or clarify a question if you don't understand completely during a phone interview.

Understand the role you are applying for and the added benefit you would provide the company if they hired you to be a part of their team. // Use LinkedIn to network with individuals that work in the company you want to join. Getting G2 on the company, any current issues or problems that you may be able to assist in solving, and getting information on the person that will interview you will all help in the interview process.

Common topic that often has some great responses. Being able to hold a conversation and not address the interviewer as a CO is pretty big. Work on your interpersonal skills. The largest issue is always veterans under-valuing themselves when it comes to salary. The military doesn't pay you much and companies know you bring a large wealth of knowledge and leadership skills into their organization. Their initial offer may seem tempting, especially when comparing it to your military salary, but do your research. Figure out what the average is for the position in your locality. Remember you can negotiate your salary; this extends to bonuses as well.

Lastly, think outside the box. The civilian world doesn't have clear cut lines and mission accomplishment will be most easily achieved when you can approach issues asymmetrically.