Are there some living things where the distinction between plant and animal is blurry or unclear? I wouldn't know where to put something like yeast. I also thought of photosynthesis, but then I heard that some salamanders have photosynthetic cells. So, what's the difference between a plant and an animal, formally?
Yeast are neither plants nor animals; they are fungi. The old classification where things were lumped into only two buckets - plants or animals - has long since broken down. In fact, even things you might think of as plants, like algae or most seaweed are no longer classified as plants. Under the old system, plants and animals were considered kingdoms, and the latest classifications now divide the Eukaryotes into six kingdoms, but even this is poorly evidenced and facing challenge.
The best method of classification is probably cladistics which is based on the evolutionary history of organisms - but even it has problems when you start considering what to do with horizontal gene transfer and endosymbiosis. Because under a cladistic view, plants and animals are defined not by their features but by their ancestors your question becomes moot, I think.
That "photosynthetic" salamander is clearly an animal, with smaller photosynthetic organism living in it symbiotically.
And yeah, cladistis is the way to go. You build your tree based on DNA, and see if the data lets you group organisms in a useful way. You might find a few organisms whose genome makes them edge cases, but this salamander is not one of them. Yeast very clearly falls way outside both categories.
Classification is not only based on one or a few features, but you have to consider lots of features in classification of livings. for example plant cells globally have chloroplast, cell wall, and vacuole and have not centrioles. Animals are different in all this features with plants. furtherly plants are autotroph and steady while animals are not. Other organisms are also different in these features or other features with plants and animals.