There were no directly incorrect assertions about Mathematica on Page 9.
However, since you are drawing me in to it, I will dispute just one of the four sections - the statement that "Maple is the uncontested leader for computing symbolic solutions to differential equations".
Firstly the justification for this has always been the results of the Kamke text. But, if I recall correctly your original work here used Kamke as the motivation (Cheb-Terrab, Duarte and da Mota, 1997). As such it is not entirely a 'representative random sample'. I have heard (though not seen for myself) that tests against other tests suites have put the ODE results much closer.
But more importantly this paragraph is premised on a tight definition of symbolic ODEs, and Mathematica's DSolve has extended in other directions to include symbolic solutions to piecewise defined/ discontinuous ODEs, ODEs with events (eg a simple bounding ball), differential algbebraic equations or delay differential equations. And, of course, if you are interested in differential equations, then numerical solutions are extremely important and Mathematica has a full FEA PDE solver with 3D mesh generation and refinement.
So while the paragraph does not contains obvious errors, it gives a rather skewed view of differential equation support.
(Such a user might also care about discrete cases where Mathematica's RSolve also goes somewhat further).