Collaborative robotics is increasingly prevalent in manufacturing, introducing complex ethical and safety challenges, alongside productivity benefits. Understanding these challenges is critical for the responsible implementation of these systems. This study presents a systematic approach to identify, categorize, and analyze these challenges. We employed a comprehensive mixed-methods framework that integrated systematic literature analysis, thematic content evaluation, and quantitative bibliometric assessment based on a corpus of 3,390 peer-reviewed publications extracted from the Scopus database. The core contribution is a hierarchical thematic coding framework encompassing four primary domains: safety, ethical, and implementation challenges and intersectional themes, with detailed subcategories and operational definitions. Our analysis revealed a high prevalence of both safety (81.9% of papers) and ethical (91.2%) considerations, often addressed concurrently (75.0%). Key specific challenges include job displacement (75.4%), psychological safety (45.7%), and human autonomy (43.9%), whereas notable research gaps exist in areas such as sensor reliability (0.7%) and decision authority (0.2%). We also mapped the predominant solution approaches to specific challenges, highlighting the reliance on safety standards and validation methods. This framework provides a methodologically robust tool for researchers and practitioners to navigate the complex landscape of ethical and safety issues in collaborative manufacturing robot design.