For those of you who don't know, working split means the DX transmits on one frequency and listens on another. This is frequently done by DX stations when the pileup (stations calling) are so numerous that it's difficult, if not impossible, to get a contact completed on a single frequency. On most bands, the split might be something like 5kHz up, or if the pileup is really big, maybe a range, like 5-10 or something. Good operators will mention their split frequency every few calls (or more frequently), though it's generally pretty obvious when a station is working split: If it's rare DX and he's working stations you don't hear on his frequency, more likely than not he's working split.
If you're in the US, things get a little trickier on 75/80m and 40m. The frequency allocations are different for the US and most of the rest of the world. In particular, on 40m, most countries outside of the US can use either CW or phone pretty much anywhere in the 40m band, though typically they'll use frequcies above around 7.050mHz. When working split, they will usually listen at 7.150 or above. US amateurs can transmit there, but while most other stations can't it's legal for anyone to listen there.
What happens quite often when someone is working split is that they may accidentally transmit where the DX is transmitting instead of listening. While there are obviously some operators who really don't understand the whole concept of split, I think that others just accidentally transmit on the wrong frequency, realize it, and move. On 40m, it's a particularly bad because if the DX is transmitting in that lower portion of the 40m band and you answer on his frequency, if you're in the US, you are out of the US phone band and in violation of the FCC rules.
Tonight, TX5C was transmitting on 7.063mHz and listening up at around 7.174 and up from there. He wasn't giving his split frequency all that often, but it was pretty obvious that he must have been working split. It seemed that every few calls, someone with a US callsign would call on his frequency, meaning that not only were they calling where the DX wasn't listening, but they were, as I mentioned, in violation of FCC rules. However, in a lot of cases, the US caller would give his callsign once, or even partially, realize what was wrong, and move to the correct frequency.
That didn't stop the dreaded DX Cops. (Thanks for AA0MZ for creating that and other great pages). As soon as the out-of-band guy would start to call, the DX Cops would jump in with great comments like "You're Out of Band!" or "Wrong VFO!" or "Press the split button!". Now I suppose, in theory, these folks might be from some country where transmitting phone on 7.063mHz is legal, but somehow I doubt it. These self-appointed DX Cops seem to feel that the slightest transgression needs instant negative feedback. Of course, not only are these guys themselves (likely) out of band, but they are also failing to identify wherever they are from. Unlike real police, who, in the course of their duties, are empowered to bypass some laws (e.g., police will exceed the speed limit to get to an accident or crime), the DX Cops aren't given any special powers, except by themselves, so they are not only in violation of the regulations requiring specific types of transmissions in a particular part of the band and of the identification requirement, but they are intentionally interfering with another station.
Tonight, it got pretty funny, since one guy in particular would jump in and "correct" the individual almost as soon as he started transmitting. The funny part was that in at least one case that I heard, the person realized their mistake immediately after their initial call to TX5C, and called on the correct frequency. As usual, Officer DX jumps in and says "XX you're out of band!". Meanwhile, as he's saying that, TX5C has just called "XX" (who obviously had switched to the correct frequency) and worked him while Officer DX was yelling at "XX" in the wrong place.
Why do they do it? Is it because they feel that they need to "police the amateur radio service"? (I know as hams, we're supposed to be self-policing, but I don't think that's what the FCC has in mind.) Is it because, as some have speculated, that they feel that they are simply superior to everyone else and have a "right" to do this? (Left as an exercise for the reader.)
I think I've figured it out: In some jurisdictions, police are required to give out a certain number of traffic citations each month for whatever reason. Apparently, these DX Cops must be part of some magic DX jurisdiction where they have a "DX Ticket quota". If they don't hand out enough "tickets", they might loose their jobs. We wouldn't want that to happen ... would we?