Let's take a break from this general job hunting stuff and talk about what happens after you'd found the job you'd love to do. It's time to apply, hopefully you have your CV in great shape already, so you just need to dash off a quick cover letter and submit it! Well, maybe you can do better than that. After I submitted a few cover letters that read more or less "I am pretty great, and you are looking for someone awesome, so..." or the one I wrote for the dairy fermentation tech "I brew beer, so I know a little about fermentation. And aseptic technique is a lot like food handling skills, right?" I've been looking into what really should go on a cover letter. There is lots out there about the format and etiquette of a cover letter, so let's focus on Content.
Much like the first year graduate student who answers questions to prove that they know lots, my first cover letters were very reactionary. My attempts to address how I fit the job requirements were just that, a binary assessment of the parallels between who they want, and who I am. This isn't helpful for either me or the person trying to hire me. Instead, I am trying think a little more about why there are these job requirements, and how I can help meet these same goals. The career seminar I went to last week was quite literal about it, "If you are applying to work at a company, they care about the bottom line, you need to explain how you will help turn a profit." Although it made me cringe after years of hanging out with academics, it is more valuable to show how I can meet the goals of the organization. If you are applying to a post-doc in an academic lab, the same is true (not about profit, but tone). Your letter should address how you and your experience can help the lab in general.
This gives you a bit more flexibility in how you describe your experiences- the job may say they need an expert in immunology, but really they need someone who can jump right into the histology with some understanding of immunology, and get expert along the way. (Because you should be applying for jobs that you might not be perfect for one day one.) This gives you a chance to highlight not only why you are great, but also that you understand the needs of the position and have given it serious thought. This isn't the same as selling out. Granted, if you don't agree with the goals of the organization or believe you have the skills or ambition to meet them, you shouldn't be applying. But if you can provide a good faith genuine explanation of why you are interested and will be successful in the job, you will be a stronger candidate for the jobs you actually want.
I've heard similar, more aggressive, advice for interviews. Specifically, at the interview, take the time to lay out how you'll start making an impact in the first 100 days. I don't think I have the confidence for that, but it is pretty easy to imagine how someone who could demonstrate that much interest and understanding during an interview is likely to get hired, right?