The basic worshipful illusion about Newton is to give him credit for rotational differential equations of motion -- the most critical part of mechanics -- which were first published by the Swiss mathematician, Leonhard Euler (1707-83), nearly a hundred years after Newton's death. (I call this "Shirley MacLaine mathematical physics".)

Athough Newton created the differential calculus (independently of Gottfried Leibnitz (1646-1716) and Pierre de Fermat (1601-1665)),

• Newton failed to give sufficient credit to his Cambridge teacher, Isaac Barrow (1630-1677), for teaching him Barrow's discoveries of the geometric ideas behind differentiation and integration;
• Newton's notation is mostly passed over;
• Newton's "proof" of the mathematics involved, implicitly, dividing by zero (as pointed out by Bishop George Berkeley -- see "neglected" at this Website);
• Newton did not use the calculus to prove his equations about solar system mechanics, but (fearing attack by academicians) used geometry , making his derivations almost inscrutable;
• much or most of his great work, Principia Mathematica, is so difficult to read (even after translation from Latin) that only a few experts understand it, and much of it is incorrect.

"Except for certain simple if important special problems, Newton gave no evidence of being able to set up differential equations of motion for mechanical systems [his italics], It is not the function of the historians to guess what Newton might have done or could have done, nor is what Mach could do with Newton's principles relevant; the cold fact is, the equations are not in Newton's book. pp. 104] To summarize: In Newton's Principia occur no equations of motion for more than two free mass-points or more than one constrained mass-point; Newton's theories of fluids are largely false; and the spinning top, the bent spring, lie altogether outside Newton's range. [93] .... The dynamics of rigid bodies, altogether avoided by Newton, was initiated earlier by the famous solution of Huyghens for the physical pendulum (1963). [104] .... Not until 1747 did Euler see, and he was the first to see, that for all discrete systems the eqwations of motion are of the form m_ka = F_k where the force F_k on the kth body is described. [167]" Essays in the History of Mechanics, Clifford Truesdell, Springer-Verlag, 1968.

Newton quit serious mathematical and physical research in mid-career, living on his sinecure as "Director of the Mint", and devoted his scholarship to study of alchemy and a numerical interpretation of The Bible. (We know this because eminent economist, Lord John Maynard Keynes, bought a box of Newton's papers at auction, studied them, and made public this evaluation of the work of Newton's latter years.)

For "second opinion", see New Foundations of Physics, David Hestenes, Kluwer Academic Publishers, Dordrecht, 1986.