"as we say in Figure 1.4 ... " => The caption of Fig 1.4 doesn't say this, but the statement can be infered from the bottom right figure. Maybe "as we show" is better?
Page 13
Caption of Fig 1.5: add "/N" to the formula for E_{RMS}
close to the end: "In Figure 1.6. We see that" => "In Figure 1.6, we see that"
Page 14
caption of Fig 1.6: "least squares" was not used before (unless I missed it). I think a short explanation what is meant by it would be good.
middle: "the chosen box was the blue one" => "the chosen box was the red one" (blue is not bad, but the discussion was about the red box)
Page 26
middle: "consider a the distribution" => remove "a" or "the"
Page 27
middle: after "common sense is violated", there's a question mark
middle: "context of of polynomial" => "context of polynomial"
in Laplace box: "he was also made" => "he has also made" (I think it would be nicer to swap Bayes box and Laplace box, because we first here about Bayes in the text, and Laplace is somehow hidden).
Page 29
middle: "X = (x_1 ..." => X should be in bold and not italic, for vector
middle: "n=1,...N" => I think it shouldn't be there at all, we don't use n before 1.46, where it's clear what it is
middle: "from a Gaussian distribution" => I think it would be more clear: "from a univariate Gaussian distribution", because we just talked about multi-variate.
Page 32
just before 1.2.5: "likelihood liesat the root" => "likelihood lies at the root"
bottom: it's a bit confusing that the presicion, which was denoted by lambda on page 28, is now denoted by beta. Maybe one of them can be changed, or maybe a little explanation would do.
Page 34
3rd line: "parameters called" => "parameters are called"
Page 36
second last line: "by a factor of M" => shouldn't it be "by a factor of S"?
Page 40
Fig 1.20: it would be nice to add M1, M2 and M3 above the corresponding curve
Page 50
Fig 1.29: in my printing I see "re ect region" (j is missing)
Page 63
2nd line above the equation (1.114): f(lamda a + ... => right parenthesis missing