I had interviewed for the Product Leader of Client-Facing products role. I applied online and after a call with the recruiter and the hiring manager, they brought me onsite for a sleight of interviews. There was a homework assignment and I had done a lot of preparation. Since they passed on me, I've posted these at feadbaq.wordpress.com/ .
The interview questions were for the most part straight forward, with the critical exception one of the Product head's questions. This is where I got tripped up. He had me look at a page on a major website and asked me verbatim "What's wrong with this page?". Well I should have asked more clarifying questions about what he meant by "wrong". I thought he was looking more for what product features could be added and proceeded to discuss what I though could be product improvements. But really what he was after was nitpicking at the layout of the search box and sizes of the various call to action buttons. Had I known he was after that level of granularity, I could've done so. So if you find yourself in this situation, just focus critiquing the minutia.