Medical disputes in veterinary practices are widespread; yet, a limited amount of research has been conducted to investigate the factors contributing to medical disputes. This study examined veterinarians’ and clients’ perceptions regarding risk factors and possible solutions to medical disputes. A total of 245 respondents from Taiwan, including 125 veterinarians and 120 clients, completed an electronic self-administered, semi-structured questionnaire in 2022. The questionnaire covered six dimensions: medical skills, complaint management, the attitudes of stakeholders during interactions, medical expenses, clients’ perspectives, and communication modes. The results highlighted significant differences in the perceptions of risk factors for inducing medical disputes and possible solutions between clients and veterinarians in veterinary practice. First, young veterinarians and clients perceived medical skills as the highest risk factor for inducing medical disputes, while experienced veterinarians disagreed (p < 0.001). In addition, veterinarians with medical dispute experience identified stakeholders’ attitudes during interactions as the top contributing factor. Second, regarding possible solutions, all veterinarians preferred offering clients cost estimates and cultivating empathy and compassion towards them. On the other hand, clients underscored the importance of obtaining informed consent for treatments and expenses and suggested that veterinarians should supply comprehensive written information to facilitate this process. This study underlies the importance of understanding stakeholders’ perceptions to mitigate medical disputes and advocates for improved communication education and training for young veterinarians. These findings provide valuable insights for veterinarians and clients, contributing to preventing and managing medical disputes in veterinary practices.