Dijkstra's algorithm fails to find the shortest path if the graph contains negative weight edges. The algorithm assumes that all edge weights are non-negative, and the presence of negative weights can lead to incorrect results and infinite loops.

In the worst case, a Binary Search Tree (BST) can become a skewed tree (like a linked list), where each node has only one child. In such a scenario, the time complexity of inserting an element becomes O(n), where n is the number of nodes in the tree.