One of the observations made about that story is that the soldiers deceive the villagers little by little until the process of making the soup is completed. The act of deception or gradual change is invoked in the interests of everyone who takes part: the final result is a meal that everyone enjoys because everyone is sharing and participating.
The question to ask yourself when you're working on gradual changes in your own environment and codebases is this: "What is the big picture?". You need to always be questioning if the incremental advances you make are taking you in the right direction, otherwise you risk becoming like the fabled story of the boiled frog: it's said that you can place a frog in cold water and slowly raise the temperature to boiling and the frog won't notice because of the gradual change, eventually being cooked.
We're all like that frog in that sense: it's easy to take our eye off the ball and let things slide, just a little, just this once -- every time.
We see this when we're under time pressure and there's "no time to write tests". Except we will have time to fix the bugs that come back afterwards. We see this when there's "no time to refactor", but we will have time to sit down and try to understand the giant ball of mud we made last week because we have to extend it this week.
We see this when we let small discriminations happen in the office: "We can't get mad at Stan for being forward with the ladies, because he's from a different generation". Until Stan has to have a chat with HR because no-one reigned him in when it was just "joking" with people who tolerated him. Also, tolerating these micro-transgressions doesn't help Stan: one day, when he has a real point to make, no-one takes him seriously because he's just the "creepy uncle in the basement office".
Pay attention to the small tasks in your day. Always do them to the best of your ability. Always question if there's a better way. Always strive to be the person your dog thinks you are.