Common Mistakes

Mistake $1$: Running BFS from every node to find diameter. That is $O(n^2)$. Use two-BFS instead. Mistake $2$: Thinking diameter always passes through the root. It does not. The longest path can be anywhere in the tree. Mistake $3$: Forgetting to handle both diameter endpoints in Tree Distances I.

You need the max of distances to both endpoints. Mistake $4$: Trying to solve Tree Distances II with BFS from each node. That times out. Use rerooting DP.