Thanks to Alexander Reisz, who has pointed out the need for many of these corrections. Readers are welcome to suggest more corrections and revisions in the comment field.
Chapter I
Page 15, Proposition 1.8: An adapted rc or lc process is measurable. The assumption of adaptedness is unnecessary because the process is always adapted to the constant filtration 
Page 39, Proposition 1.35: This proposition may not make sense as stated. It is about moving a random variable outside a stochastic integral. The problem is that it may not be possible to define the integral from s to t as a difference in this case. The proof seems to interpret this integral correctly, though.
Chapter II: Itô Calculus
Chapter III: Gaussian Processes
Page 104, bottom: Misprint: exp(K(s)) instead of K(s). This error may have been repeated elsewhere.
Chapter IV
Page 141: Line 7: Misprint in the equation, between the two equality signs.
Page 156: Exercise 4.3, and its solution: There is an error in the application of Itô’s lemma and a sign error.
Page 142: Cheng did not quite look at the version of Ball-Torous that I am looking at. She discounted by dividing by the value of a Ball-Torous bond, but her other asset was lognormal.
Page 144: Line 2: Misprint: B = Ball-Torous.
Page 163: Harrison and Kreps actually did not do the doubling strategy within the Black-Scholes model. That analysis may have been due to Chi-fu Huang.
Chapter V
Bottom of page 185: The equation is strictly speaking not correct because the stuff inside the conditional expectation on the right hand side may not be integrable.
Chapter VI
There are a bunch of misprints in the solutions to the exercises in this chapter.
Page 205: Proposition 6.2, Proof: The drift is 
Page 207: The relative dispersion, and the elasticity, are not necessarily positive. For a put option, for example, the delta, the relative dispersion, and the elasticity are negative. The volatility is the absolute value of the relative dispersion.
Page 219: The displayed inequality just below the middle of the page should be reversed.
Page 224: Theta negative. “A shorter time to maturity does not affect the mean … ” Not true.
Page 227: Next to last paragraph: same issue.
Chapter VII: Gaussian Term Structure Models
Page 253: The time interval should be [t,u], not [u,t]. This occurs twice on the same page.
Page 253: Yield curve increasing: f > R, yield curve decreasing: f < R.
Page 255: Proposition 7.3 should be Proposition 7.5.
Page 265: Top paragraph, lower curve and higher curve are mixed up.
Page 274: In the displayed equations in the middle of the page and just below, s and t are mixed up.
Page 276: The reason why the partial derivative of R with respect to sigma is negative is that as sigma increases, the money market account becomes riskier, whereas the bond held to maturity is riskless.
Page 285: f is a quadratic function of tau, not of r.
Page 291, middle: Merton has alpha and sigma constant. In the third-to-last displayed equation, ds should be du. Remember that e to the power K, and alpha, are functions of u.
Page 291: I the expression expression for f(t), there is one right parenthesis too may.
Page 292: There is a mispring in the formula for $m$.
Page 292: In the displayed equation defining the function P(r,s;t), write P(r,s;t) instead of P(r(s),s;t).
Page 292: It is cumbersome to compute the derivative of A(s;t) with respect to s. But interchange the order of integration between x and u. That makes it easier. I believe Shreve does something like that.
Page 294: In the third-to-last group of displayed equations, there should be no e to the power K in the second line.
Page 295: In the Merton model, mu should be replaced by alpha.
page 296: Second and third displayed equations: one subscript t is missing in each.
Around here, I can replace continuous differentiability by absolute continuity.
Page 297: In the verification of the HJM result in the extended Vasicek model, there is a sigma missing under the integral sign on the RHS of the first equation, and on the next line, sigma should be squared.
Page 297: Proposition 7.8. It looks like the last term in the last equation is simply v(s;t).
Page 304: In the equation for forward rates in he middle of the page, brackets are missing on the right-hand side.
Page 306: In the second-to-last displayed equation, there is a minus sign missing in front of A(s,t). The equation just before that can be rewritten by computing the inner integral. The resulting expression will be simpler, especially when calculating the drift of P.
Page 308: In the group of three displayed lines, there should be no minus sign at the beginning of the second line.
Page 308: The equation in the middle of the page misses a term: r(t)-r(s).
Page 309: According to Heitmann and Trautmann (1995), the continuous-time limit of the Ho-Lee model was independently derived by Jamshidian (1991) and by Heath, Jarrow, and Morton (1992).
Page 315: The zero-coupon bond yield goes to r, not zero, as tau goes to zero.
Appendix A: Measure and Probability
Page 317: Statement 2, put n under bigcup.
Appendix B
Appendix C
Black (1976) derives a PDE for the value of a commodity contract (or is it the forward price?). It is similar to the Black-Scholes PDE with one term missing because the value of a futures contract is zero. He solves it with the terminal condition. According to footnote 8, another boundary condition and a regularity condition are needed to make the solution unique. He gives the boundary condition but not the regularity condition. He says the need for these additional conditions was not noted in Black and Scholes. He also uses the PDE method to find the value of a forward contract.
Appendix D: Suggested Solutions to Exercises
Page 403: Next to last displayed equation: There should be a 2 in the denominator
Page 406: Same story.
Page 409: Exercise 6.8: The notation: T-t = tau has not been introduced.
In the second-to-last line of the solution, d_2 tends to minus infinity, not to zero.
Page 416: In the group of three displayed lines just below the middle of the page, r is missing at the beginning of the second and third lines.
Page 418: Third line: B(x,t) instead of B(s,t).
Page 419: Second line to third line on the page, now you deduce … Not obvious.
References and Index
Misprint in the index: Anold instead of Arnold.
One Comment
1. p326, Prop A.10
The symbol between the F’s should be the set product symbol, not the measure product symbol.
2. p328, Section A.3
” … the expression a<<b means that a_i < b_i for every i=1,…,n"
The last character should be k, not n.