The rapid expansion of foundation models (FMs), such as large language models (LLMs), has given rise to FMware, software systems that integrate FM(s) as core components. While building demonstration-level FMware is relatively straightforward, transitioning to production-ready systems presents numerous challenges, including reliability, high implementation costs, scalability, and compliance with privacy regulations. Our paper conducts a semi-structured thematic synthesis to identify key challenges in productionizing FMware across diverse data sources, including our industry experience developing FMArts, a FMware lifecycle engineering platform, and its integration into Huawei Cloud; grey literature; academic publications; hands-on involvement in the Open Platform for Enterprise AI (OPEA); organizing the AIware conference and bootcamp; and co-leading the ISO SPDX SBOM working group on AI and datasets. We identify critical issues in FM(s) selection, data and model alignment, prompt engineering, agent orchestration, system testing, and deployment, alongside cross-cutting concerns such as memory management, observability, and feedback integration. We discuss necessary technologies and strategies to address these challenges and offer guidance to enable the transition from demonstration systems to scalable, production-ready FMware solutions. Our findings underscore the importance of continued research and multi-industry collaboration to advance the development of production-ready FMware.