Here's one I hadn't run into before.
The typical hotel broadband access service checks the MAC address of your computer. When you first connect, it sees the new MAC address, interrupts whatever access you were about to make and instead delivers a sign-up screen. After you've signed up, your packets are routed directly to and from the Internet until your sign up period expires.
Of course this means every packet is being inspected to verify the MAC address is for a computer that has paid for access. This is very light packet inspection, nothing like the DPI that various ISPs have been called to task for. It's also very fast so it doesn't introduce noticeable latency, at least until now.
Last night I was staying in the InterContinental Nehru Place in Delhi and I observed a strange effect on perhaps 1 out of 3 or 1 out of 4 page loads. First I would see a very brief splash screen from the hotel's ISP, then my desired web page would load. This was unusual but not a bother. Next, while using Bloglines, every now and then the left screen list of unread posts would fail to refresh, instead displaying a message about access had timed out. However the next refresh always worked, so again, I can live with that.
Finally I tried to create a blog post but I lost the text as I went to post it. Ugh! Apparently, Typepad's blog author's content posting page requires reasonably fast turn around time for update messages.
Clearly MAC address redirection was beginning and then being canceled. I'd never run into anything like that before -- a case where even shallow packet inspection is a problem.