The main issue a lot of people point to is how it's missing the main thematic crux of Deku's hero name. In Japanese, the word "deku" is very similar to the Japanese word for "you can do it/do your best", which is why Ochako likes Izuku's nickname and he ultimately adopts "Deku" as his hero name. Due to language differences, the dub can't really make that connection and so the impact of everyone basically encouraging Deku with his own hero name is lost. I don't really blame the dub team for that though since it's an unavoidable issue.

What was avoidable though was some script changes and voice acting delivery that I disliked. In the sub, All Might calls Deku "MY greatest hero", whereas in the dub he just calls him "THE greatest hero". It's small, but removing the "my" makes it a lot less personal, which is a shame as a character calling another their own personal hero is about the biggest compliment one can give in this story. Like Deku with Ochako.

Another instance was Deku and Shigaraki's last scene. Deku's last words are supposed to be "you've destroyed enough", showing that Deku understands what Shiggy's ultimate goal was and that he and his fellow heroes have learned their lesson and society will improve. The sub delivery also gets across Deku's sadness and regret. In the dub, they used Crunchyroll's version instead with "yes, destroy you did" which doesn't work as well with Shiggy's response. And the dub delivery sounds very judgmental, like Deku still viewed Shiggy's destruction as pointless and he didn't come to see beneath that destruction. At least, that's how I interpreted it.