Integrating AI into a leadership style is not without its potential challenges.

Below are some key points that could arise:

1. Understanding AI Capabilities and Limitations: One of the primary challenges is understanding what AI can and cannot do. Leaders may have unrealistic expectations about AI, which can lead to disappointment and failure of implementation. This requires a continuous learning mindset and staying updated with the rapidly evolving field of AI.
2. Cultural Shift and Employee Resistance: Implementing AI may bring about significant changes in the way an organization operates, which can result in resistance from employees. Leaders will need to manage change effectively, reassuring employees about their roles, and providing necessary training.
3. Ethical and Legal Implications: AI can raise numerous ethical and legal issues, such as privacy concerns, bias in AI decision-making, and potential job losses due to automation. Leaders need to be well-versed in these issues to ensure that AI is integrated in a responsible and legal manner.
4. Technical Infrastructure: Depending on the existing infrastructure of a company, integrating AI might require significant technical changes. This can pose challenges in terms of cost, time, and technical feasibility.
5. Data Management: AI typically relies on large amounts of data for training and operation. Managers will need to ensure that they have reliable methods for data collection, storage, analysis, and protection. In addition, data quality and relevance can significantly impact AI's effectiveness.
6. Skill Gap: There might be a gap in the necessary skills needed to effectively implement and use AI within an organization. This could require investing in training for existing staff or hiring new talent with AI expertise.
7. Decision-Making Process: AI can dramatically change the decision-making process in organizations. Leaders will need to balance relying on AI-driven insights while maintaining their judgment and critical thinking skills.
8. ROI Justification: AI projects can be expensive and it may be challenging for managers to demonstrate the return on investment, especially in the early stages of implementation.
9. Security Risks: With AI integration comes increased digitalization, which in turn can lead to heightened security risks. Managers need to be mindful of these threats and ensure appropriate safeguards are in place.
10. Maintaining Control: As AI systems become more advanced, ensuring that human operators maintain control and understand the decision-making process of the AI can be challenging. This is often referred to as the "black box" problem in AI.

Navigating these challenges requires a strong understanding of both the specific AI technology being used and the broader organizational context in which it's being implemented. Effective communication, thoughtful planning, and proactive management can all help leaders successfully integrate AI into their leadership styles.