The responses so far in this thread seem to say to Clemnet either a) it's goofy/quirky, and that's good, so learn to love it!, or b) what about that 13th hole, huh? He asks a lot of good questions, but I haven't seen any good answers which are on point - a rarity in this group, I hasten to add! - apart perhaps from ChrisB's post early on in the thread.
I myself really like the 16th green, first and foremost because of its uniqueness. Sure, it isn't always fair to the golfer - although I believe different sections of the green are easier to hit from different sides of the fairway, which encourages a semblance of strategy from the tee. Too, there are good misses and bad misses on every hole and on every shot; this green tends to magnify the bad misses (which if memory serves means anything to the right of the green when the pin is front or back), which is a good thing. Most importantly, for me, the 16th green gets away with something you wouldn't get away with on a modern design because it came into being before golf course architecture became an art as such. North Berwick is almost the equivalent of a cave painting in terms of its antiquity - a very stylistic cave painting, mind you, but still something very early in the evolution of architecture. There weren't rules to follow or schools of thought to emulate...the course mostly just is, because that's mostly how it was when it began. There's something wonderfully refreshing about that, isn't there?
That said, I've begun to think North Berwick gets too much of a free pass from critics on this site. On my most recent visit there, I was struck by how mundane a lot of the terrain is - there are many wonderful contours on the property, but there are also a number of flat fields with little character which pass as fairways, and a number of ordinary greens which don't really pass muster. I'm not sure if any course in the world with holes as sublime as the Pit and the Redan is as uneven in terms of general quality from hole to hole. It's a unique place and well worth seeing, but I think it must be very difficult to rate it highly (among the Top 50 in GB&I, say) unless you turn a very blind eye to its weaknesses.
Cheers,
Darren