Possible error in Hatfield's "Quantum Field Theory of Point Particles and Strings"? In problem 8.1 of Hatfield's Quantum Field Theory of Point Particles and Strings, the reader is tasked with calculating the trace $$\operatorname {tr}(\gamma_0\frac{(\not p_2 + m)}{2m}\gamma_0\frac{(\not p_1 +m)}{2m}).\tag{problem 8.1}$$ Hatfield says that one should obtain the result  $$\frac 1 {m^2}(8E_1E_2-p_1\cdot p_2 +4m^2),\tag{problem 8.1}$$ where the dot product is that of $4$-vectors. However, when I calculate this trace, I find that I get $$\frac 1 {4m^2}(8E_1E_2 - p_1\cdot p_2 +4m^2),$$ which is off by a factor of $4$. I can find no error in my calculation, and this leads me to believe that Hatfield's calculation is wrong. Which of these is correct?
Edit: Here is my calculation. First we factor out a $\frac 1 {4m^2}$ from the trace to get $$\frac 1 {4m^2}\operatorname {tr}(\gamma_0(\not p_2+m)\gamma_0(\not p_1 +m))=\frac 1 {4m^2}(4m^2 +\operatorname {tr}(\gamma_0\gamma^\mu p_{2\mu}\gamma_0\gamma^\nu p_{1\nu})),$$ since all the trace terms linear in $\not p$ vanish ($\operatorname {tr}\gamma^\mu = 0).$ Next invoke the Clifford algebra to obtain $\gamma^0 \gamma^\mu = 2g^{0\mu}-\gamma^\mu\gamma^0$, insert this into the trace on the RHS, and after much algebra (which is simple to do, provided one recalls the trace identity $\operatorname {tr} \gamma^\mu\gamma^\nu = 4g^{\mu\nu}$) one finds this equals $$\frac 1 {4m^2}(8p_{2 ,0}p_{1,\nu}g^{0\nu} - 4g^{\mu\nu}p_{2,\mu}p_{1,\nu}+4m^2) =\frac 1 {4m^2}(8E_1E_2-4p_1\cdotp p_2 +4m^2). $$
 A: 
Hatfield says that one should obtain the result  $$\frac 1 {m^2}(8E_1E_2-p_1\cdot p_2 +4m^2)$$

Your steps are correct and that is a typo. Omitting the $4m^2$ term in the denominator for now,
$$\text{Tr}\left[\gamma_0(\not\vec p_2+m) \gamma_0(\not\vec p_1+m)\right]=\text{Tr}\left[ (\gamma_0\not\vec p_2\gamma_0)+\gamma_0 m\gamma_0)(\not\vec p_1+m)\right]$$ Now if you expand this, you'll be left with $$\text{Tr}(\gamma_0\not\vec p_2\gamma_0\not\vec p_1+\gamma_0m\gamma_0\not\vec p_1 +m\gamma_0\not\vec p_2\gamma_0+\gamma_0m\gamma_0 m)= \ \text{Tr}(\gamma_0\not\vec p_2\gamma_0\not\vec p_1+m\not\vec p_1+m\gamma_0\not\vec p_2\gamma_0+m^2)$$
and if you make no algebraic errors, the term
$$\text{Tr}(\gamma_0\not\vec p_2\gamma_0\not\vec p_1+m\not\vec p_1+m\gamma_0\not\vec p_2\gamma_0+m^2)$$ leads to the final result $$\frac{1}{m^2}(2E_1E_2-\vec p_1\cdot\vec p_2 +m^2)$$
where the $\frac{1}{4m^2}$ factor is now inserted.
Also, you wrote

However, when I calculate this trace, I find that I get $$\frac 1 {4m^2}(8E_1E_2 - p_1\cdot p_2 +4m^2),$$

which appears to be missing a coefficient of $4$ on the second term.
