When I was starting college I took an analysis course based on Kolmogorov and Fomin. We didn't work with all sorts of special functions, but focused much more on functional analysis, measure, and multidimensional functions. Later we did Fourier transforms for any locally compact abelian group. What's important in math changes.
But this specific book only covers elementary-to-intermediate topics in Algebra, Geometry and Calculus from the looks of it. It isn't likely to change as much at all.
Books can have mistakes. Other editions could correct these mistakes, provide more elegant proofs, more fruitful approaches to solving problems, more understandable language, or more standard terminology.
Assuming it’s Carr’s, IIRC it’s a rather odd style of work, it’s a summary of the state of basic mathematics rather than a textbook per se, with pages of theorems with little explanation.
So a modern version would at most be a different idea of what the core theorems should be.
Note the massive errata list which is very likely just the scratching the surface. Later editions tend to either implement these corrections, or have a more complete list.
