High levels of inequality are a problem—messing up economic incentives, tilting democracies in favor of powerful interests, and undercutting the ideal that all people are created equal.
This review is a pleasantly level-headed assessment, but I wish Gates expanded a bit more on the core issue of why high inequality is a problem.
"messing up economic incentives"
How does high inequality affect incentives differently than moderate inequality, which most people agree is acceptable? Extremely wealthy people do not buy up all the shoes. Firms do not abandon the giant market of individuals of modest means when very wealthy consumers appear.
"tilting democracies in favor of powerful interests"
This also happens at small scales and becomes more visible at a large scale. It appears to me a problem with democracy: it promises something it cannot deliver. Swatting down the most powerful special interests means the next tier of special interests will take over. Do we suppose they will cause less harmful distortion?
"undercutting the ideal that all people are created equal"
If an ideal is true, it can stand up for itself. Bill Gates himself proves the benefit that can accrue to the world when health, intelligence, connections, family resources, and luck defy the ideal and gather in one person. There is a potential down side here, of course, but there are far more wealthy philanthropists and benign art collectors than wicked CEOs bent on destruction.