It's backed by fascist psychopath Peter Thiel and it, at least for a long time, promoted a crypto scam as a main browser feature.

Additionally to the other two replies, Brave also injected referral IDs to an URI when you directly typed it in. Allegedly it was a mistake and they put it behind a toggle:

• Article: https://www.technewsworld.com/story/brave-browser-caught-redirecting-urls-for-cash-86701.html
• Their blog: https://brave.com/blog/referral-codes-in-suggested-sites/

Also, per default the new tab page shows advertisements in the background. Firefox does also show ads on the new tab page in the link grid, so it's a bad thing both do and you can disable it on both. But with an almost-full-window sized ad Brave managed to make that worse still.

Is Brave Legit? | Controversies and Features explained.

Aside from the homophobia, Brave also runs an ad network. I am skeptical about their privacy claims when they profit off the data to sell ads.

Essentially nothing. People on here tend to be alarmist when it comes to it, but when you actually dig into the negative claims, they are all either vastly overblown or misconstrued.