Course-based undergraduate research experiences (CUREs) offer an expanding avenue to engage students in real-world scientific practices. Increasingly, CUREs are instructed by graduate teaching assistants (TAs), yet TAs may be underprepared to facilitate and face unique barriers when teaching CUREs. Consequently, unless TAs are provided professional development (PD) and resources to teach CUREs effectively, they and their students may not reap the assumed benefits of CURE instruction. Here, we describe three perspectives -- that of the CURE TA, the CURE designer/facilitator, and the CURE student -- that are collectively intended to inform the development of tentative components of CURE TA PD. We compare these perspectives to previous studies in the literature in an effort to identify commonalities across all sources and offer potential insights for advancing CURE TA PD efforts across a diversity of institutional environments. We propose that the most effective CURE TA PD programs will promote the use of CURE-specific instructional strategies as benchmarks for guiding change in teaching practices and should focus on three major elements: 1) enhancement of research and teaching acumen, 2) development of effective and inclusive mentoring practices, and 3) identification and understanding of the factors that make CUREs a unique learning experience.