As I go through this film shot by shot, one of the things that keeps jumping out at me is how much re-used animation there is. It's fairly well hidden as the animation is placed over a new background and the story material is different, but this film probably re-uses more animation from itself than any other Disney feature.
I don't know if the re-use was Woolie Reitherman's idea or not, but he certainly endorsed it. In all the features that list him as a director, re-use is present. In Reitherman's later films, he lifted animation from earlier features and usually had it cleaned it up for use as a different character, though there are spots where animation is lifted without changes. There are websites (here, here and here) devoted to documenting Disney re-use.
The reason for it boils down to money. The feature before 101 Dalmatians was Sleeping Beauty. That film was in production for many years as Walt Disney was seemingly more interested in Disneyland than he was in the movie. As a result, the expenses were high and the resulting box office did not meet expectations. There was a massive layoff when Sleeping Beauty was finished and there was some question as to whether the studio would continue to make animated features.
As a result, the financial pressure on 101 Dalmatians to come in at a significantly lower cost was strong. The introduction of the Xerox process was done to save money, as the inking department could be laid off. Xerography also made the animation of the puppies far more efficient as they could be repeated. The fact that cels are not truly transparent always restricted animated scenes to four or five cel levels before the background colour was degraded unacceptably. Today, the puppies could all be animated individually and there is no limit to how many levels could be digitally composited, but when you've got dozens of dogs on the screen and only five possible cel levels, life becomes a lot more complicated.
Here's just a few examples from this sequence of animation re-use. The first and third images below are from the current sequence. The second and fourth images are from earlier in the film, where the animation originated.