The most common problems are usually not dramatic. They are things like vague bullets, weak action verbs, unclear impact, too much text, inconsistent formatting, and content that feels impressive only if someone already knows the context.
Another frequent issue is trying to sound important instead of sounding specific. Consulting reviewers tend to respond much better to concrete, well-evidenced achievements than to inflated language.
A strong resume makes it easy for the reader to understand what you did, why it mattered, and what that says about your potential. You may also find it helpful to read how consultants review resumes if you want a more structured way to practice this.