This report is a digest of the DOE/NSF Workshop on Correctness in Scientific Computing (CSC'23) held on June 17, 2023, as part of the Federated Computing Research Conference (FCRC) 2023. CSC was conceived by DOE and NSF to address the growing concerns about correctness among those who employ computational methods to perform large-scale scientific simulations. These concerns have escalated, given the complexity, scale, and heterogeneity of today's HPC software and hardware. If correctness is not proactively addressed, there is the risk of producing flawed science on top of unacceptable productivity losses faced by computational scientists and engineers. HPC systems are beginning to include data-driven methods, including machine learning and surrogate models, and their impact on overall HPC system correctness was also felt urgent to discuss. Stakeholders of correctness in this space were identified to belong to several sub-disciplines of computer science; from computer architecture researchers who design special-purpose hardware that offers high energy efficiencies; numerical algorithm designers who develop efficient computational schemes based on reduced precision as well as reduced data movement; all the way to researchers in programming language and formal methods who seek methodologies for correct compilation and verification. To include attendees with such a diverse set of backgrounds, CSC was held during the Federated Computing Research Conference (FCRC) 2023.