List of a few key errata:

There is a missing squared in the proof of 3.7.1.  Try to find it.

Proposition 5.2.4, proof, should have "nd | (ad-bd)" instead of "ad-bd | nd".
Thanks to Phillip Poplin for noticing.

The proof of 12.4.2 has an error in the last line, which should start
2^{[(2^n-1)-1]/2}; thanks to George Jennings.

Fact 14.2.1 is exactly opposite the truth, I believe.

The formula Hilbert-Waring in 14.2.8 should have 2^m+floor((3/2)^m)-2; 
the exponent inside the floor is missing.

The explanation of Figure 16.3.5 is for Lagrange's Table IV, not Table III.

The statement of Theorem 19.2.5 has an obvious typo of e^i instead of e_i
in the formula for \sigma_0 .

I know there are some in exercises but I have not collated them into a 
single document.