Retracted research discussed on social media can spread misinformation. Yet we lack an understanding of how retracted articles are mentioned by academic and non-academic users. This is especially relevant on Twitter due to the platform's prominent role in science communication. Here, we analyze the pre- and post-retraction differences in Twitter attention and engagement metrics for over 3,800 retracted English-language articles alongside comparable non-retracted articles. We subset these findings according to five user types detected by our supervised learning classifier: members of the public, academics, bots, science practitioners, and science communicators. We find that retracted articles receive greater user attention (tweet count) and engagement (likes, retweets, and replies) than non-retracted articles, especially among members of the public and bots, with the majority of user engagement happening before retraction. Our results highlight the prominent role of non-experts in discussions of retracted research and suggest an opportunity for social media platforms to contribute towards early detection of problematic scientific research online.