Everyone likes innovation and will rah-rah for it until it gores their ox. The misalignment of incentives and innovation is always the biggest problem. Technology challenges can always be beaten into submission. Real innovation is by definition upsetting to the status quo, and it takes intestinal fortitude on the part of the leadership (not management, _leadership_) to face the incentive issue and get the org properly aligned around change.
I believe that one of the biggest challenges when considering innovation is to maintain an innovative mindset whilst still being able to adhere to a company strategy and business model. Certainly there will be many innovations which in and of themselves are very good but the skill is in making sure that whilst it may be a "neat idea" or "novel solution" that it actually address a need, rather than simply an alternative which may be more risky. This means that some ideas will need to be rejected or put on hold which is where maintaining the innovative mindset within the business becomes a challenge.
Happy to follow up with a call.
Truly being innovative is very difficult and presents most people or companies with a series of challenges. In mind the biggest is maintaining it.
Innovation means always being uncomfortable and constantly disrupting yourself. I see a lot of startups or entrepreneurial people who WERE innovative and used it to create a company or rise up the ranks but then became comfortable with the thing they did get there. Eventually others catch up and they are no longer innovative or disruptive despite thinking they are. Innovation is a mindset that's easy to lose when comfortable or successful so pushing people to thrive on that edge of discomfort is critical
Secondly innovation is all relative so you need to make sure that the peer set you are surrounded by is pushing it to the limits. If you are surrounded by people comfortable with the status quo then very incremental changes will seem much more drastic or impactful as they are in reality. It's important to create the right contexts and in this case use social pressure to be 'more innovative' as something that pushes (without taking this to the extreme).
Happy to discuss innovation or building the write innovation culture more in depth. There's a lot of other components like how incentives are set up etc.