My reply is below:
..All of the answers so far have been very valuable. As an industry guru, executive and trainer, I always seem to take things back to the "root" level. Remember, that an interview is simply a sales call! In this case, it's the candidate's turn to do the selling (as opposed to the recruiter, if one was involved). In sales, we learn that we need to prospect and then qualify an account in order to, amongst other things, understand, in essence, what it is that they want to hear in order to be sold to... in other words, what are their hot buttons. Sale people then know, that ANYTHING that they sell should address those hot buttons! If you work with a recruiter, they should be able to provide you with those hot buttons. If they don't know, then they aren't that good and you should ask them to find out for you. However, once you go on the interview, the odds are that you already found them out or learned even more than you were told.... This can either be learned because the employer "tipped" their hand or because they asked you very specific questions and then later explained why.. in "tipping the hand", the employer often will TELL YOU why they are about to ask a question or they will talk about what they are interviewing for.. For ex, they may say "Natalia. We really need people who don't make mistakes and are diligent.... we don't have the time or the resources to check on work that has been completed".. As an aside, this is very bad for a hiring manager to do since the smart interviewee will pick up on this and make that one of their strengths. My point is that during the process you should listen and now know what it is that they want...
At this stage, after you give your feedback to a recruiter, the good recruiter will take notes and then make sure that they know all of the hot buttons. It seems as though you may be a recruiter. If so, it is NOW that you need to listen to what the candidate just told you and go back to your original job order notes.. Then, knowing that the selling doesn't stop until the deal is done, you (or the candidate) need to craft a specific thank you note and SPECIFIC references that actually address the SPECIFIC hot buttons for this one job. This is why pre-generic reference checks don't help with a specific deal.. So, even if references were checked, you should go back to the reference and ask them for specific examples about how meticulous they were (using the above hot button example) and also get sound-bytes for any other hot buttons. The thank you letter should also provide examples.
This combination of "after interview" work will be the best way to "move your name to the top of that list". It is always sales.. Sales, Sales, Sales!