Public policy-making is indeed a complex endeavor that attempts to apply systematic methods of political analysis to address societal problems. Political analysis provides frameworks and tools to understand the distribution of power, interests, values, and institutions that shape policy choices. However, the journey from policy formulation to implementation is fraught with challenges, particularly concerning the internal dynamics of the bureaucracy and the diverse interests of stakeholders.

Application of Political Analysis to Policy Areas: Political analysis helps in understanding:

1. Problem Definition: How political actors frame issues, which problems gain attention, and whose definitions prevail.
2. Agenda Setting: The political processes by which certain issues make it onto the government's agenda while others are ignored.
3. Policy Formulation: The influence of various political ideologies, interest groups, and power structures on the design of policy alternatives.
4. Decision-Making: The political bargaining, negotiation, and coalition-building that lead to the selection of a particular policy option.
5. Policy Evaluation: Assessing not just the technical effectiveness but also the political acceptability and distributional impacts of policies.

Concerns with Processes Inside the Bureaucracy: Once a policy is formulated, its implementation largely rests with the bureaucracy, which is far from a neutral, mechanistic actor. Internal bureaucratic processes introduce significant complexities:

1. Bureaucratic Discretion: Bureaucrats, especially at the street level, have considerable discretion in interpreting and applying policies. Their personal values, professional norms, and organizational culture can significantly shape how policies are delivered, sometimes deviating from the original intent.
2. Organizational Culture and Routines: Established bureaucratic routines, hierarchies, and organizational cultures can create inertia, resisting change or new policy directives. Inter-agency rivalries and 'turf wars' can also hinder effective coordination required for complex policies.
3. Information Asymmetry: Bureaucrats often possess specialized knowledge and information that political principals lack. This can give them leverage, allowing them to influence policy choices and implementation in ways that serve their organizational interests.
4. Capacity and Resources: The effectiveness of policy implementation is heavily dependent on the administrative capacity, human resources, and financial resources available within the bureaucracy. Lack of these can lead to implementation gaps.
5. Resistance to Change: Bureaucrats may resist policies that threaten their established routines, power bases, or perceived interests, leading to passive resistance or selective implementation.

Concerns with Stakeholders: Public policy-making is inherently a multi-actor process involving a wide array of stakeholders, each with their own interests, resources, and influence:

1. Diverse and Conflicting Interests: Stakeholders (e.g., interest groups, businesses, NGOs, citizens, media) have varied and often conflicting interests regarding policy outcomes. Policy-making becomes a process of negotiation, compromise, and sometimes outright conflict among these groups.
2. Power Imbalances: Not all stakeholders have equal power or access to decision-makers. Well-organized, well-funded groups can exert disproportionate influence, potentially leading to policies that favor specific interests over the broader public good.
3. Lobbying and Advocacy: Stakeholders actively engage in lobbying, advocacy, and public campaigns to influence policy decisions. This introduces political considerations that may not always align with rational policy analysis or evidence-based approaches.
4. Public Opinion and Legitimacy: Policy-makers must consider public opinion and the need for political legitimacy. Policies that are technically sound but lack public support may be difficult to implement or sustain.
5. Accountability: Ensuring accountability to diverse stakeholders, especially when policies involve multiple actors and complex implementation chains, is a significant challenge. Different stakeholders may hold different actors accountable for different aspects of a policy.

In conclusion, while political analysis provides essential tools for understanding the 'what' and 'why' of policy choices, the 'how' of policy implementation is profoundly shaped by the intricate internal workings of the bureaucracy and the dynamic interplay of various stakeholder interests. Effective public policy-making, therefore, requires not only robust analytical skills but also astute political acumen to navigate these complex bureaucratic and stakeholder landscapes, balancing competing demands and managing the inherent tensions between technical rationality and political feasibility.