We explore the citation activity and social media engagement of retracted and non-retracted scientific research publications. While prior research has mainly studied retraction trends among specific areas of research, author countries, and publication venues, we focus on Twitter activity differences between retracted and non-retracted publications across all of science. We analyze over 62,000 research publications and 60,000 tweets that contain links to publications in their posts. Our findings highlight that citations and tweet activity are not correlated (i.e., high academic impact does not imply high social media impact), and that temporal trends of publication counts and tweet counts differ. Comparing tweet text from retracted and non-retracted publications, we train a random forest classifier that achieves 0.92 accuracy in predicting if a tweet references a retracted or non-retracted publication.