No matter whether you think the specification is weak or is not reflective of the functional design intent it is not technically wrong. As Jeff pointed out the symbols are consistent with the 1982 standard so the datum feature designations and the use of the (S) symbol would not be wrong if the specification declared that standard.
•Align the coordinate system to the primary datum feature surface A.
•Set translational origin at the center of the (.88) radius segment B.
•Stop rotation by aligning to the center of the (.53) radius segment C.
To inspect the position of C (dia .010 S) relative to A|B you would compare the measured distance between the axes of the two radial surface segments to their basic distance which is 9.177 or (-.35^2+9.17^2)^0.5. Next you would double that error to make it a diameter value consistent with the diameter tolerance and compare that value to the tolerance limit (.010 regardless of feature size).
To inspect the two hole diameter positions (dia .040 M) relative to A|B|C you must first rotate the coordinate system about the axis of datum feature B to the basic angle relative to datum feature C which is tan-1(-.35/9.17) or ~ -2.1858 degrees.
•Compare the X and Y coordinates of the (.875) diameter hole to its (X,Y) basic location ( 0,0) compute the radial displacement, double it, and compare that value to its variable tolerance limit (.040 + actual hole size-.87).
•Compare the X and Y coordinates of the (.625) diameter hole to its (X,Y) basic location (- .35,9.17) compute the radial displacement, double it, and compare that value to its variable tolerance limit (.040 + actual hole size-.62).
I agree with some of the previous comments and am skeptical that the choice of datum features for this specification actually reflect the functional constraints in assembly. I would also point out to the customer that deriving axis (especially datum feature axes) from limited circular segments of the surface (approximately 180 degrees for B) and (approximately 160 degrees for C) is not good design or measurement practice.