Memory allocation issues in a TypeScript application can manifest as high memory usage, memory leaks, or out-of-memory errors. To debug such issues, you can leverage Node.js's built-in memory profiling tools. Start by running the application with the `--inspect` flag, which allows you to use Chrome DevTools to take heap snapshots and track memory allocations over time. These snapshots help identify objects that are retained in memory and pinpoint the source of leaks. Another option is to use the `heapdump` or `memwatch-next` libraries to programmatically capture and analyze memory usage. If you're working with large datasets, avoid loading entire collections into memory at once, and instead use streams to process data incrementally. Additionally, watch for global variables, which can hold onto memory unnecessarily, and always clean up resources like database connections and file handles after use. Mastering memory management is critical to building scalable and efficient TypeScript applications.