Overlapping IPs
A number of years ago I received a call saying that we couldn't reach a well-known-museum-based-in-South-Kensington's web site from our internal LAN via our proxy servers but it worked fine from the wifi network on the campus.
After much head scratching & eventually getting hold of someone at aforementioned museum I discovered that they were using the same IP range for their internal network as had been allocated to us for our public addresses and therefore NAT addresses. Consequentially return traffic was being routed to their internal LAN and not back to us... This took quite a bit of explaining...
(The Wireless wasn't affected as it was on a different subnet)
Once I'd discovered this I could re-program the NAT router to use a different set of IP specifically for traffic to the museum while they set about a program to renumber internally. This work-around was fine until I had to hand back the address space that I was using for the work-around and the problem resurfaced.... (in fairness they'd only had 2 years to renumber at this point)