The correct answer is B) Check bearing lube oil temperatures. The main propulsion reduction gears on a vessel require continuous monitoring of the bearing lube oil temperatures. This is a critical operational check to ensure the proper lubrication and cooling of the reduction gears, which are under high loads and speeds. Bearing failure due to overheating can lead to catastrophic damage to the propulsion system. Regulations and best practices require engineers to continuously monitor bearing lube oil temperatures and take corrective action if temperatures rise outside of the normal operating range. The other options, while important checks, do not need to be performed continuously. Radial bearing wear, gear alignment, and inspection for pitting/scuffing are typically done at regular maintenance intervals, not on a continuous basis.