I think the OP was referring to the ship crossing over the target sled they were towing, off of Pearl Harbor.
In that incident, Queeg ordered the rudder put over to head back to Pearl. However, he never gave the helmsman the order to steady up on a course as he was too busy berating Horrible for the untucked shirt tail. The helmsman isn't allowed to steady up on his own, so he kept the helm over. That turned the ship in a circle. The ship's turned radius was 1000 yards. The target sled they were towing had a 2000 yard cable (according to the book). That meant that the ship cut across it's own tow cable.
The main cause for concern would have been the cable wrapping itself in the propellers and/or the rudder, which would leave the ship unable to maneuver. That would mean they'd either need a tug to bring them in, or put divers over the side to try and untangle the screws.
The reactions of Meatball and Chief Budge were exaggerated, I think, as they knew nothing cataclysmic would happen. Maryk was concerned because of possible damage to the ship's steering/propulsion gear. I wouldn't say he was panicked though. Concerned and surprised, but not panicked.
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