Whatever problems you uncover, the most important thing is to ask yourself how your role relates to these issues. How can you do your work in a way that helps alleviate some of the issues you’ve discovered? Are you in a position to directly affect any of these things simply by virtue of being a new person? Simply by being aware of these issues, you’re bound to find new ways you can improve the business directly or indirectly.
There is a simple but effective process I like to use to quickly speed up the learning curve in a new company. It’s called a “positioning map”, and it is a means of plotting your company visually against its competitors based on the strategies that each are pursuing. The graphic is simple; the effort lies in distilling your competitors’ strategies well enough to group them along strategic dimensions.