One of the regular duties of grad students and postdocs is to interview candidate lab members. I wasn't ever actually trained to conduct proper interviews, but I primarily focused on figuring out whether folks would be a good 'fit' for the lab in terms of personality and work-ethic. The candidate's scientific 'skillz' were important, of course, but since such positions are theoretically all about learning new skills or improving old ones, specific knowledge seemed less important than evaluating someone's capacity to learn.
Flash-forward to the present: Now I'm interviewing candidates for industry positions and things are a bit different. As I was told by friends and colleagues who'd made the jump to industry, biotech companies generally try to find people with the skills required to fill specific positions , such as someone with the experience necessary to run high-throughput drug screens on cell-lines, for example. This is typically made clear in the job posting, which lists both required and preferred skills. Ultimately, while asking for a particular skill set is well and good, anyone who has looked over lists of job postings knows that some of these sets are about as common as unicorns .
Determining whether a candidate with fit in with the team culture remains as important in a company as it does in a lab. However, unlike in the lab, we aren't all working in our own vacuums. Folks in our team divvy up tasks, share resources, and collaborate on getting the job done. So, while the opportunity to learn continues to exist in abundance (I've been benefitting immensely from it!), there is a trade-off in hiring someone who may take months, instead of weeks, to get up to speed - even if they're brilliant and clearly a great fit. This is probably a good thing to keep in mind if you're ever frustrated with the interview process. Sometimes companies are focused on a specific set of skills, and not getting a job isn't necessarily a reflection of your quality as a candidate. Mind you, I realize that that's little consolation.
Switching topics a bit - I have noticed some little interview details that folks looking to get into industry may want to consider. First, I work with some of the smartest people that I've ever met. Industry is not the place where academic failures end up: like in academia, publications and results show that you can get the job done. You're still likely selling yourself as a scientist, so think about how you're portraying yourself before saying that you're tired of 'academic research' or 'writing papers'.
Secondly, company hiring committees are much more interested in the technical details of a candidate's work - after all, it's highly unlikely that you're moving to a company to continue your current research program. People will ask why you chose to analyze data in this way, or why you applied this or that statistical test. It goes without saying that everyone should understand the underlying logic behind their work. However, this is particularly important when the basis of the interview may be to determine how much they really know about that about that which they claim to be an expert. Saying that someone 'told you to do it like this' or that may be a deal breaker.
Finally, from my own experiences with grad-school and postdoctoral interviews, they tend to be a bit more casual than their industry counterparts. This should be obvious, but dress up  and leave the lab/intra-field gossip at home.
 In a Q. and A. with, Richard Sheller, former VP of Research at Genentech and now at 23&me, I asked whether he thought that hiring to fill specific roles in industry was a good thing. He told me that he felt that since biotech projects are always in flux, he'd been trying to steer his managers towards focusing on adaptability rather than specific skill sets. However, managers are responsible for getting projects done - so it was unlikely that much was going to change.
 For example, I saw a posting for a Ph.D. level scientist who had bench-top genomics experience, solid coding skills in at least Python and Java, and experience maintaining large-scale databases in mySQL. I'm sure such people exist, but wow.
 I'm amazed by how casually some people will dress when giving invited seminars or during faculty candidate interviews. It's a fine line: I don't think that we should all be wearing suits and ties, but graphic tees and sneakers are a bit much, no? The awkward flipside, of course, is that if you're interviewing in Silicon Valley, all of your interviewers will be dressed like they're going to a BBQ. Them's the breaks, I guess.