It's not the problem, it's the response
Every company I have worked with has faced its share of problems. If everything is easy, it probably means you aren't trying hard enough. Whether you are trying to push technology into areas not yet explored, selling to customers who are wary of small companies, forging a partnership with a much bigger company, or just trying to be as productive as possible with a small amount of resources, every small company faces problems.
I don't judge companies by their problems (or lack of problems). Instead, I look at their response to problems. What communication style does the CEO and management team employ? Does the CEO start making all the decisions, like a field general? Or, does the CEO pull the team in close and forge consensus on the path forward? You can find successful examples of both styles, but I bet that the second style has a higher chance of success.
One key to me is how much the company is willing to change in order to focus on its key priority. Will they get employees to back off from their normal tasks in order to put more effort onto the big issue? Can they keep up morale as people do jobs that aren't their top desire or main occupation? During these times of crisis, you can learn a lot about how a company really works. These are the times that the wheels can fall off of the bus if you don't have a strong team.
Another great indicator is how the CEO deals with the Board and other advisors. Do they get defensive and keep information to themselves? Or, do they open up and bring in outside help? This is one of the trickiest questions because the outside help can also take up a lot of time and be a distraction. There is usually no shortage of people who can offer help if only you can spend several hours bringing them up to speed. If you do this a few times, you have wasted a lot of valuable time. This is where the CEO has to triage with one or two key Board members to gain agreement on the action plan. Bringing in a couple of key people from outside can make a huge difference in some situations. But, bringing some partner from your venture firm up to date so that the person on your Board can cover their butt is a waste of time.
I usually like to have one or two engaged outside Board members on every company Board of Directors. I like experienced executives who come from the company's industry and have good mentoring skills. These people will already be up to speed on the company and can provide a lot of targeted advice during difficult times. And, the CEO should already trust them and be used to opening up to them.
One of the hardest things to do is to plan ahead for crises. You can't be sure what type of crisis may come up, but at least make sure you have some good independent Board members and advisors who stay up to speed on the company so you can put them to use quickly when you really need them.