I don’t see the point to doing brain teasers. I find that open-ended questions intended to get the employee talking will be good things. At the second interview, you have to figure that they’re qualified on paper for the position. Now you want to find out if they are creative, smart, a team player, a good communicator, or whatever.
Ask them questions about how they have handled in the past a situation – for example, solving a difficult problem, creating an innovative solution, needing to work with a peer to get a job completed, experiences with management, how did they handle a stressful time, how do they multitask, or even just ask them their opinions about what a good leader is or what does being a team player mean. Really, the important part is to get them talking and they will either impress you, bore you, or set off red flags.
If they answer in only a few words, encouage them to talk more about the situation. If they can’t, that for me is a red flag. They aren’t thinking through the questions.
If they have a very hard time explaining themselves, that to me is also a red flag. You want to allow for people being nervous, but a good employee should always be able to tell you why they did something or when they succeeded. If they didn’t, they’re going to need handholding at least and at worst just have very poor job ethics and don’t care.
A good applicant will be prepared and able to speak up about what is good about themselves but without being overconfident (I am great at everything, I have no weaknesses, I don’t need help ever).
I always find that asking them why they want to work for your company is a positive question. Believe it or not, I’ve often found major concerns from that question – people who don’t really want the job and are reluctant probably are just going to keep looking. I’ve had some people admit even that they didn’t like the job and just needed money. If in doubt, follow up with asking how this job would fit into their plans for the next five to ten years. Usually, people who are lying about whether they want the job won’t be able to clearly answer this.
I also think it’s a really good idea to explain the good, bad, and ugly about the job also. What’s the point of going through the whole hiring process if they can’t handle it or won’t be able to stand it? Reasonable expectations should be set.