Contemporary scientific media production requires a complex socio-technical infrastructure we call the "Media Production Pipeline" (MPP). Media professionals engage with researchers along the MPP to disseminate science news to the lay public. However, differing incentive structures and professional contexts frequently set researchers' values and needs at odds with those of media professionals, resulting in problematic or failed interactions. We ask the research question: what pain points in scientific media production afford opportunities for future HCI innovation? We then present a grounded theory analysis of 24 interviews with researchers and media professionals, yielding several key contributions. First, we describe two collaborative domains in scientific media production between research advocates and media outlets. Second, we characterize discrete technological gaps and pain points in both domains. Finally, we discuss implications for design and propose solutions from HCI areas like peer production, online communities, recommender systems, and online collaboration.