Despite the emergence and rapid growth in popularity of data mesh in recent years, it is still a relatively new concept and there is still a lot of research to be done before it is fully explored. In particular it is unclear how a complete data mesh can be successfully implemented. As a first step, it is necessary to identify open implementation challenges in order to identify research gaps that will point researchers in the right direction. In particular, it is important to consider both literature and practical applications as sources of knowledge. To this end, we conducted a literature review and interviews with industry experts from a globally operating industrial company. Thereby we focused on the technical challenges associated with implementing a data mesh in a company with a well-established data infrastructure. In addition, we derived research gaps from these challenges that need to be addressed in future work.