Are they busy?
A great software engineer will be loaded with projects. This comes from years of successful projects, as well as the repeat and referral business generated from good, quality work. Someone who is overly excited or eager to meet may not be in demand, which could be a very bad thing.
Can they show you their work?
A given for any software designer or programmer is a wide variety of work across many different industries, unless they happen to be a specialist in one just one area. They will also have deployed many development, testing and production environments, so their should be at least a couple of those types of projects available that they could demo for you.
Can they relate, communicate and facilitate?
A hallmark of any effective person is their ability to work well with others. Effective people relate to others using their communication skills and actually improve any process they are a part of. If the software engineer you are interviewing is not capable of explaining a problem and a raft of possible solutions, they will never be able to work well with all levels of your own organization.
What is their origin story?
A full time custom software engineer should be able to tell you of the great battles they fought to get where they are today. No, they are not superheroes, but they should have faced circumstances or challenges that took some fortitude to overcome. Obviously, no two origin stories are alike, but something in their story should be reminiscent of your own business' origin or growth story.
Are they both costly and cost effective?
Any one charging a below market rate should be avoided. There is a reason they are below market, either they are not fully in charge of their time (and consequently, yours) or they are still learning the ropes of coding, database design or user interfaces. I hate to use the house analogy, but would you prefer an electrician or plumber who is affordable or one who is effective?
What won't they do?
They must be forthcoming about skills they don't have or traits that they themselves feel are subpar. There is no one person who is a solution for all problems you face today or possibly in the future. If you don't receive an immediate response to this question, they are probably just trying to figure out which of the things they know of that you are least likely to object to.
Have they failed?
This is not a question about overcoming obstacles. Every reputable software engineer has a project that failed and perhaps even failed horribly. It could be from circumstances they could control or not. It doesn't matter. They should be able to dissect everything that happened for you and explain it in great detail because although it was a failed project, it was still a technical exercise.
How do they balance work and life?
Honestly, you are looking for a programmer who is happy, in both work and life. All of us get the same number of hours every day and every year, but some can accomplish so much more because they are diligent about time management. Another way to look at this question is, how many times have you solved a vexing problem by stepping away? You want someone is strong enough mentally to know when to step away, or when to step in.