Ooh, I had a good one just recently. There was an awesome exhibition at a nearby museum. It had loads of old Greek and Roman stuff, and was really well put together. DH and I spent about six hours there, I think. It was lots of fun.
After we'd been there a while, we noticed one particular young man (he looked about 20) following us rather closely. DH and I would stop at a coin display or something and read everything and talk about the coins to each other. This strange man would also stop and pretend to look at the coins, until we moved on. Then his friends would catch up and he would replay everything DH and I said (we have an interest in these kinds of things, so we know a lot of weird trivia) to them, going on about, "oh, if you knew as much about these things as someone like me..."
His friends would ooh and aah, and then he'd stalk us to whatever display we were currently at and repeat the whole thing. It was very bizarre. We both decided quietly that we'd ignore it, since he probably wouldn't last too long--we take ages as we enjoy ourselves and like to take everything in, and most people would get bored if they tried to take as long.
At one point, there was a set of ancient records in Latin, over two thousand years old. DH is competent at ancient Greek, and I at Latin, so we normally translate for each other. This particular piece was nice and easy, and of course our shadow listened to everything. We move on as his friends catch up, and all of a sudden he comes storming over to us.
"How dare you! You guys are idiots!"
It turns out, he had forgotten what the translation was, so he'd made something up (he'd been making a lot of things up while showing off), but one of his friends knew enough school Latin to call him out on it. And so we are the bad guys because he can't remember a translation he eavesdropped on. Shame on us for upsetting the special little snowflake. The security guard shushed him, and he left shortly afterwards, proclaiming the exhibit to be boring and inaccurate (I'm not sure how authentic artifacts are inaccurate, but there you are). We giggled for quite a while.