Huge amounts of data is generated with the emergence of new sensors technologies. Human Activity Recognition (HAR) data sets are generated from cameras, such as video or still images, capturing human behaviour through sensors like gyroscope, Bluetooth, sound sensors, and accelerometers. These generated data sources are collected by the researchers and formed into open data sets. However, these data sets often show issues during data set construction, sharing, searching, that could produce further challenges for reuse of the data by others. The main objective of this research is to explore the current issues and challenges faced by researchers in the HAR domain. A detail literature review was conducted to extract information from the published literature. Similarly, a questionnaire survey was sent to selected researchers having expertise in the HAR domain and who work with open data sets. The main issues and challenges were identified and classified into a hierarchical structure. This research will help HAR researchers to be aware of the current issues and challenges in the field of HAR open data sets. It will help to promote important attributes applicable to many open data sets, such as privacy, anonymity, platform maintenance, data sets descriptions, metadata, environmental conditions, resources, and training, while constructing and sharing new data sets.