I've now read this cover to cover once, and many individual sections multiple times, and taught an upper division course from the book. I like it; it's a really really good textbook. It's especially notable for being outstandingly clear in its prose and mathematics (though there's a couple spots where he should make clear he's being illustrative rather than rigorous). But I also get the feeling that something holds it back from being a *truly wonderful* undergrad textbook, an adjective I'd apply to Schroeder's Thermal Physics or Griffiths's Introduction to Electrodynamics. But it's hard to put my finger on exactly what holds it back a bit.
I think I can identify three things that I wished it had achieved, but that it didn't quite. I don't know that I would know how to fix two of them, while the third is easily remedied by reading this along side other texts or exercises.
First, there is a lack of cohesiveness leading to a narrative satisfaction that highlights the beauty of the field. For comparison, Schroeder does this admirably for Thermal Physics. When you finish Schroeder's book, having reasoned your way to Bose-Einstein Condensates, simulated magnets, and stood on the edge of black holes, you might look back and notice the humble beginnings: a thermometer, or a particle moving through space. You notice how much you can do with simple ideas, and the beauty snaps into place, as it had intermittently throughout the book. Taylor doesn't achieve this sense of wonder in his writing as a whole (though he does for many individual sections), which is a little unfortunate, because I do think that many teaching physicists (myself included) fail to get the beauty across amidst all the difficult nuts and bolts. However, I have no idea how to achieve a better textbook structure in this regard for this particular course; I'm not a skilled enough writer to see that.
Second, I find myself a little dissatisfied with how long it takes to get to truly novel (i.e., totally distinct from Physics I) material (from the student point of view). I totally understand why Taylor does this -- most of our students need that review and to see that it can be taken further than it was in Physics I if they develop their math skills -- but it also seems to leave insufficient time for students to internalize the truly new ways of thinking about mechanics. I think I'd like to see things like Lagrangian mechanics earlier, but I have no idea how to achieve that perfectly in practice. (Other authors do attempt to achieve things like this, but I don't think they achieve the clarity of Taylor, so I dunno if it is really an improvement.)
Finally, while Taylor often computes things numerically, he rarely suggests that the reader should. This is perhaps the only way in which the book feels dated. There are many sections for which adding even a few sentences and problems about using a programming language to achieve the results would enhance the clarity and prod the reader to numerically explore things. However, it is very easy to supplement Taylor with such explorations, so this isn't much of a drawback (I simply occasionally asked students to use Python Jupyter notebooks to investigate interesting differential equations). To return to my examples in the first paragraph, Griffith's E&M has this same failing, but Schroeder's Thermo gets it just right.