It is essential to manage memory effectively while dealing with C++ queues. Memory leaks are a frequent problem that developers encounter when working with dynamically allocated arrays inside of structs. Without proper deletion, heap memory remains allocated, leading to performance issues. Another challenge is the unexpected change in memory addresses when objects are pushed into a queue, which happens due to deep copies. Understanding how to manage heap memory using smart pointers or move semantics helps avoid unnecessary duplication and ensures optimal performance.