The second author would like to draw your attention to:
Figure 10.4: This figure has extraneous vertical lines probably caused by a printing problem.
Chapter 10 Section 1.1: The slices mentioned here are central slices. They do not include the translations associated with an IUR probe. The interested reader may consult this enjoyable reference, A.J. Baddeley,"A Crash Course in Stochastic Geometry", in Proceedings Seminaire Europeen de Statistique: Stochastic Geometry, likelihood and computation O.E. Barnesdorff-Nielsen, W.S. Kendall and M.N.M. vanLieshout, eds.(CRC Press [Chapman and Hall] Boca Raton, FL 1999).
Chapters 2,5 and 10: The chapter numbers are omitted from the problem numbers. e.g "1)" instead of "5.1)".
Chapter 6 Section 9.3 Paragraph 1: The word "be" should read "by" so that the phrase reads "bias caused by the shape".
Chapter 4 figure 4.10: This figure is confusing because the reader is viewing tangent to to the y-z plane. In the drawing, the polar angle appears to be taken with respect to the y-axis but is in fact taken with respect to the z-axis.
Chapter 3 Section 1.2: When re-typeset at the factory to change pagination, a systematic error in the book occurred. 
A symbol for set intersection was replaced by a vertical line.
Additional examples of this error occur in Eqn.(3.1a,b), Axiom 3 page 80, Eqn.(3.14) and Appendix page 468 at the definition of the Cantor Set.
Chapter 3 Eqn(3.13): Another systematic typsetting error occurs. 
The symbol for the reflection of a set is replaced by a superscripted left perenthesis. Additional examples of this error occur in Eqns.(3.16-20).
Chapter6 Eqn(6.140): The power of t in the denominator should be unity.
Chapter 5 page 147 footnote: The name, Philofsky is mispelled Philofshy.
Preface: John Cahn makes this correction to John Hilliard's biography:
"We never
overlapped
at MIT. He studied at Liverpool with Walter Owen. When Walter came to
MIT
in 1951 as a visiting prof, John came along and stayed till 1956 as a
post-doc (paid graduate assistant wages) with Morris Cohen and Ben
Averbach. Mats Hillert was one of the graduate students, and I think
John
shared an office with him, leading to much confusion. In 1956 John
came to
GE in Walter Hibbard's group, and stayed till 1962 to go to NU.
I got my PhD at Berkeley, and came to David Turnbull's group at GE in
1954
after two years at the U of Chicago. Early in 1956 Turnbull heard
Hillert
give a talk about the nucleation theory in his thesis, and came back
quite
disturbed. He asked me to look into it, and I couldn't make any sense
of
it either. I think that someone suggested I talk to John about it.
That
is how we began to work together. I left GE for MIT in 1964.
"
Chapter 10 Section 3: John Hilliard used a different and more intuitive counting convention for faces; viz. he did not count the complement of the figure (the background) as a face. His treatment is self-consistent but differs from standard use. Consequently, the constant on the r.h.s of Eqn.(10.11) is unity rather than 2, the Euler characteristic. For a pleasant discussion of conventional graph theory read R.L. Trudeau, Introduction to Graph Theory, Dover (1993). See also L.K. Barrett and C.S. Yust, "Some Fundamental Ideas in Topology and their application to problems in metallography",Metallography 3 (1970) 1-33.
Chapter 5, Problem 5.28, Eqn.(51.42P): The result can be mis-read read as the projected length of a line in 3-D which is: 
The hitch is that the 3-D projected length of a line is its projection onto a line rather than its projection onto a plane. See Problem 1.8 in E.B.V. Jensen, Local Stereology (World Scientific, Singapore, 1998).
Chapter 5 Eqn(5.66): A non-systematic error occurs. The correct version of the equation is shown here. 
The argument (2n+3) should read (2n+2) as it does elsewhere, e.g. Eqn.(5.78).
Chapter 5 Eqn(5.73): A non-systematic error occurs. The correct version of the equation is shown here.
The last index should read n3 rather than n since n3 rather than n occurs in the summation.
Chapter 5 Eqn(5.75): A non-systematic error occurs. The correct version of the equation is shown here.
The zonal harmonics are defined in terms of the cosine as shown on the l.h. side. The cosine was omitted.
Chapter 5 Eqn(5.77): A non-systematic error occurs. The correct version of the equation is shown here.
The ratio containing 4n1+1 shoud be to the right of the sign indicating summation over n1.
I want to give my sincerest thanks to Jiri Janacek for notifying me of these last four errors in Chapter 5.