The silver shovel showed up in my island early on in the game, and I didn't know enough to know I needed to grab it right away that exact day or else, so I didn't. That's about the extent of my rare item encounters.
I'm not sure really, probably all the holiday, DLC and other items I've been given by my Japanese friends and from generous people with Korean and American games on here who allowed me over to their towns during events to get the gifts from Isabelle. I own a few full 7-11 sets and some random pieces from them (I didn't cheat to get them, I brought sets and one Japanese friend had downloaded them herself but didn't like all the items so gave some to me), sloppy set which I won in a Christmas giveaway on here and another set I brought on here along with the cardboard set. I got the Chinese Zodiac animals from a friend who TT on one of their towns and a few extras from my own cycle town, same with my full hybrid seed bag set, throwing beans and unorderable stationary. TT can get you some items fairly quickly.
I guess some of the European holiday items I have like the holiday stocking and veggie basket would be considered rare to non European players.