- Wrong heap type: Max-heap for k smallest, min-heap for k largest seems backward but is correct for maintaining k elements.
- Forgetting heap property after modification: Don't modify heap elements directly.
Extract, modify, reinsert to maintain heap property.
- Not handling equal elements: When multiple elements have same priority, ensure consistent handling (FIFO or by secondary key).
- Heap size off by one: When maintaining size k, check boundary conditions for when heap has fewer than k elements.