One key thing that tends to happen in Sherlock is that there are regular displays of how inept the Police are, because for some reason we need a constant reminder that Sherlock is smarter than they are. It's rather unnecessary, since we already shown that Sherlock is incredibly clever in every episode and with every investigation. Sure Elementary went slightly down this path with them showing that the British Police were lazy, but they do something different for the American Police. In a post-9/11 America, you don't call the Police stupid. Even if you did, the viewer would never buy it since we have a bucketload of Police procedural television shows on the air, plus shows such as CSI which show the Police conducting very smart investigations. Elementary maintains this position, and the Sherlock Holmes in this version doesn't have to tell them about the basic elements of the investigation like "don't touch the body, its evidence!" Basically, Elementary has Holmes brought in as a contractor, to aid in investigations that they just don't get. But in Sherlock, he gets brought in because the case is downright odd. It is a key difference, and one which reflects on the police and the abilities of the Holmes' in the two different series. Elementary shows the Police being clever and able to investigate. This just means that you can then have Police as proper characters in the show, again something you can attribute to the additional hours it has to fill. Sure, Tommy Gregson fills the mould of every central police officer you've ever seen in an American police procedural show, but that's also a really good mould.
