The first & most important one will be managing the people/team/stakeholders or maybe a combination of all. If you are the project manager(& I am assuming you have a fairly experienced & competent team- mind you the two may not come together), you need to have skill in this area. In general a technically knowledgeable person may not have the softer variety of skill needed to manage people as he/she does not pick that up in technical education. This needs experience & learning from mistakes. That is why we pick a project manager, because of the experience! One way to learn this skill is by adopting a Coach approach, rather than a Manager’s direct & control style. A coach approach when used by a project leader(don’t want to use the word manager), takes a questioning mode, instead of jumping in with solutions.
For instance, when some team member needs help, instead of assuming what they need & jumping in with the solution/answer/plan/next steps etc., ask “how can I help you?” or “what do you want from me?”. A coach encourages the team to come out with solutions & stays in the background, thereby building team cohesion. If you know cricket its the difference between styles of Greg Chappel & Gary Kirsten!
The second important challenge is Scope management. Scope creep is a big issue. The best way to tackle this is at Planning by creating a proper WBS, involving all stakeholders, collaboratively, so that an agreement is reached on all scope items. This should be a comprehensive exercise & is vital to avoid claims that can come up later on. A Stakeholder Management & Communication Management exercise should be gone through before taking up the Scope
The third but not the least challenge is managing project constraints or impediments or risks, call it what you may. Identifying & planning responses to potential issues that can come up on the project, at the Planning stage itself, is imperative for project control. This exercise is not one time & needs to be done at a regular frequency throughout the project duration. Risk management is about prevention!
This is not exhaustive but can be said to be critical for project success
A final word. Adopting a Hybrid Lean approach avoids many challenges on projects. Such an approach, addresses the team & impediments challenges as part of the methodology. The project is broken down to weekly iterations & corrective/preventive action is taken based on daily lessons learned.