I'm an E5 at a big tech company. When I flag problems to my Director (my skip-level's manager), he brushes them off.
Examples:
What's a productive way to flag problems so they get addressed?
First question, how much do you care? How much should you care? If there are other ways to resolve the issue (e.g. talk to another manager, talk to the team, etc), those will likely be faster and easier.
In terms of talking to the director, my advice is to focus on "dynamic over substance". The way you present your concern makes a big difference in how it is perceived.
Rahul, you're a genius! When my Director brought up his top priorities in our 1:1, I told him that I have an idea for improving one of them but was worried about complaining too much. He said it's not complaining if I bring ideas on how to solve the problems -- he likes to hear any and all ideas. I immediately pulled up our 1:1 doc where I had coincidentally written down the "Problem" and "Solution" the night before. He helped me refine my solution in the 1:1 brainstorming session and even suggested a person to contact as a next step for getting buy-in. I had almost given up on raising concerns with this Director, but you've empowered me!