A couple of occasions spring to mind where the aircraft did throw in the odd niggle. One was hovering alongside a ship on a hot day in the Adriatic, when one of the engines decided to have a rest. I was perched in the cargo door at the time, as we were cross-decking stores, when I heard the engine wind down just above my head. Not fun, and it was only thanks to a very good pilot that I didn't get my feet wet.
Then there was an occasion when I was instructing an observer, we were flying over Mounts Bay. The main rotor gearbox dumped all its oil (this was not the usual common or garden leak) and we had to land asap at Penzance heliport.
Later on the gearbox was fitted with an emergency lubrication system - ELS, which gave it longer in the air before it would seize completely. (I'm not an expert on Sea King tech, so if I've got any of this wrong, sorry!)
As an aside, I recall another day in the Adriatic when we decided to do a little survival test, in a pre-ELS Sea King. We climbed to our 10,000 foot ceiling, where the cab felt very waffly and uncomfortable (so did I). The plan was then to autorotate down, simulating a total loss of main gearbox oil, to see if we would be able to reach the surface before the gearbox completely seized, the rotor stopped, and we turned into a flying brick.
We ran out of time with quite a long way still to go...