How do you empower your team to learn to spot opportunities that on the surface, appear as problems or anomalies?

This is a tricky space. First, ensure you have the right metrics in place. Metrics drive behavior. If you have metrics on ideas, innovations or even out-of-the-box solutions you can trigger a new mindset on your team.
I have found that when they mention a problem they are thinking on the day-to-day common solutions. They start by complaining about the problem. That triggers negative thoughts.
I always ask them to explain the problem with real life examples. From the end user point of view. That causes them to set the mindset in the shoes of the person or area with the problem. Then, ask them to throw the wildest idea on how it can be solved. With a few refinement, usually all those “crazy” ideas have part or even the full solution. They think may not be accepted or that it will be “judged”.
So, it is not to empower them, is to ask them to think about those ideas.

I empower my team to view problems and anomalies as potential opportunities by fostering a culture of curiosity and continuous learning. Whenever we encounter unexpected behavior—whether in systems, processes, or data—I encourage them to dig deeper, ask "why," and consider the broader context rather than jumping straight to resolution. In team discussions and post-incident reviews, we highlight examples where a so-called "issue" led to a valuable insight or innovation. I also promote psychological safety so team members feel comfortable sharing observations and hypotheses, even if they're unconventional. Over time, this mindset shift helps them naturally see that anomalies often reveal hidden inefficiencies, unmet needs, or new ways to improve services—a crucial skill in today’s evolving IT landscape. 

Curiosity is the key! Collaborating with our customers, partners, and within IT are essential to fully understand the context, problem statement, and opportunities. Ensuring that the team is supported to experiment, learn, and adapt are essential ingredients to fostering an innovation environment. Not all issues or problems can be associated with 'innovation'; however, having that mindset is helpful and quite frankly, more fun!

I encourage them to step back and ask why before jumping straight into solution mode.