Well, one common element is the tough and grizzled detective. He's often a loner, with a bit of a drinking problem perhaps. Another is the seedy underbelly of the city that gets explored, like dark alleys and smoky bars. And there's usually a damsel in distress that the cop has to save, either from a gangster or some other bad guy.
Typical elements include a detective who's a bit of an outsider. In a cliche old time cop story, he might not play by the rules all the time. There are also often femme fatales who try to mislead the cop. The settings are usually the grittier parts of town, like run - down bars and abandoned warehouses.
One way is to play with the mystery aspect. Instead of a simple murder mystery, make it a complex web of crimes that are all connected in unexpected ways. Also, develop the relationships between the characters more deeply. For example, the relationship between the cop and the informant could be more than just a business deal. They could become friends or have a shared past. The writer can also add some historical elements to the story to make it more engaging, like basing it on a real - life crime wave in a particular era.
You can make it interesting by subverting the cliches. Instead of the detective always being the hero, make him have some flaws that really impact the story. And instead of the typical 'good guys vs bad guys' scenario, add some moral ambiguity to the characters and their actions.
I'm not sure which specific 'the old salty cop story' you're referring to. There could be many stories about an old and experienced cop that might be described as 'salty' in the sense of being tough or world - weary.
In a cliche Christmas story, you'll often find the element of redemption. For instance, a character who has made mistakes in the past gets a chance to make up for it during the Christmas season. There's also the use of Christmas symbols like Christmas trees, snow, and bells to set the mood. And of course, there's always a happy ending. Whether it's a family getting back together, a person finding love, or just a general feeling of hope and joy at the end of the story.