When facing 'Out of Memory' errors in Hadoop, it's crucial to inspect the 'mapreduce.map.java.opts' configuration parameter. This parameter determines the Java options for map tasks and can be adjusted to allocate more memory, helping to address memory-related issues in MapReduce jobs.

Sqoop can streamline the process of migrating legacy data from multiple databases into Hadoop by using the Multi-table Import functionality. It enables the concurrent import of data from multiple tables, simplifying the migration process and improving efficiency.

Advanced Hadoop applications often leverage Apache Spark for real-time data processing and analytics. Apache Spark is a powerful open-source data processing engine that provides high-level APIs for distributed data processing, making it suitable for complex analytics tasks.

The choice of file block size impacts Hadoop cluster capacity by influencing the efficiency of data storage and retrieval. Larger block sizes can lead to better storage utilization and reduced metadata overhead, increasing the overall capacity of the Hadoop cluster.

In Scala, the Scalding library is commonly used for interacting with Hadoop and performing big data processing. Scalding provides a higher-level abstraction over Hadoop's MapReduce, making it more convenient for Scala developers to work with large datasets.

For real-time data syncing between Hadoop and RDBMS, Sqoop can be integrated with Apache Kafka. Kafka enables the seamless and real-time transfer of data between Hadoop and relational databases, supporting continuous data integration.

Apache Pig's optimization mechanism is crucial for efficiently processing large volumes of data. It includes various optimizations like predicate pushdown and filter pushdown to enhance the performance of Pig scripts.

In scenarios where data processing efficiency is crucial, MapReduce is often the most effective Hadoop programming paradigm. It excels at processing large datasets in a distributed and parallel fashion, making it suitable for scenarios prioritizing efficiency over real-time processing capabilities.

In a Hadoop cluster, Zookeeper Nodes are crucial for maintaining continuous operation and data accessibility. Zookeeper is a distributed coordination service that helps manage and synchronize distributed systems, ensuring the coordination of tasks and maintaining cluster stability.

Apache Spark performs computations in-memory, which is a key improvement over the MapReduce model. This in-memory processing reduces the need for intermediate disk storage, resulting in faster data processing and analysis.