The 1st and 2nd editions of Sacks' Saturated Model Theory are quite similar. In the introduction, Sacks mentions as changes only "numerous corrections, mostly typographical, some mathematical."
However, the proof of Proposition 31.2 has been replaced with a much more sophisticated proof of a weaker statement. But as far as I can tell, the original proof is valid. Is there an error I'm missing, or is there some other reason why he might have made this change?
Background. Here is Sacks' notation in chapter 31:
$T$ is a complete countable substructure-complete theory. $\mathcal{K}(T)$ is the category of substructures of models of $T$, with the maps being monomorphisms. $S\mathcal{A}$, with $\mathcal{A}\in\mathcal{K}(T)$, is the Stone space of $\mathcal{A}$. $S$ is a contravariant functor from $\mathcal{K}(T)$ to $\mathcal{H}$, the category of compact Hausdorff spaces and surjective maps.
$DS\mathcal{A}$ is the Morley derivative of $S\mathcal{A}$. Sacks shows that we can iterate $D$ transfinitely, so $D^\alpha S$ is also a contravariant functor from $\mathcal{K}(T)$ to $\mathcal{H}$. The details don't matter for this question, just that $S\mathcal{A}\supset DS\mathcal{A}\supset D^2S\mathcal{A}\supset\ldots$ is a decreasing sequence, strictly decreasing until it stabilizes at an ordinal called the Morley rank. Hence the Morley rank is at most $\text{card}\,S\mathcal{A}$ (although this is not used in the proof below).
Suppose $\mathcal{V},\mathcal{W}\in\mathcal{K}(T)$ and $i:\mathcal{V}\subset\mathcal{W}$ is the inclusion map. We say $x\in D^\alpha S\mathcal{V}$ splits in $D^\alpha S\mathcal{W}$ if $(D^\alpha Si)^{-1}(x)$ has at least two elements.
If $\mathcal{V}$ is the smallest object in $\mathcal{K}(T)$ containing a finite set $Y$, then we say $\mathcal{V}$ is finitely generated.
$\mathcal{U}$ is a universal domain if for every finitely generated $\mathcal{V}\subset\mathcal{U}$, every ordinal $\alpha$, and every isolated $x\in\mathcal{V}$, if $x$ splits in some $D^\alpha S\mathcal{W}$, then $x$ splits in some $D^\alpha S\mathcal{W}^*$ with $\mathcal{W}^*\subset\mathcal{U}$, $\mathcal{W}^*$ finitely generated.
The proof of Prop. 31.2 uses this proposition, which is the same in both editions:
Proposition 31.1. If $x\in D^\alpha S\mathcal{V}$ and $x$ splits in $D^\alpha S\mathcal{W}$ for some $\mathcal{W}\in\mathcal{K}(T)$, then $x$ splits in $D^\alpha S\mathcal{W}^*$ for some $\mathcal{W}^*$ finitely generated over $\mathcal{V}$.
The 1st ed. version:
Proposition 31.2. If $\mathcal{A}\in\mathcal{K}(T)$ is infinite, then there exists a universal domain $\mathcal{U}\supset\mathcal{A}$ such tbat $\text{card}\,\mathcal{U} = \text{card}\,\mathcal{A}$.
Proof. Let $\kappa=\text{card}\,\mathcal{A}$. A chain $\{\mathcal{U}_\delta | \delta<\kappa\}$ is defined by induction on $\delta$. $\mathcal{U} = \bigcup\{\mathcal{U}_\delta | \delta<\kappa\}$.
$\mathcal{U}_0=\mathcal{A}$.
$\mathcal{U}_\lambda = \bigcup\{\mathcal{U}_\delta | \delta<\lambda\}$.
For each ordinal $\alpha$, each finitely generated $\mathcal{V}\subset\mathcal{U}_\delta$, and each isolated $x\in D^\alpha S\mathcal{V}$, use 31.1 to choose a $\mathcal{W}_{\alpha,x}^V$ finitely generated over $\mathcal{V}$ with the following property: if $x$ splits in $D^\alpha S\mathcal{W}$ for some $\mathcal{W}\in\mathcal{K}(T)$, then $x$ splits in $\mathcal{W}_{\alpha,x}^V$. Let $\mathcal{U}_{\delta+1}$ be the least member of $\mathcal{K}(T)$ whose universe contains
$$U_\delta\cup\bigcup\{\mathcal{W}_{\alpha,x}^V | \alpha, V , x\}$$.
Assume $\text{card}\,\mathcal{U}_\delta=\kappa$ in order to see $\text{card}\,\mathcal{U}_{\delta+1}=\kappa$. The cardinality of $\{\mathcal{V} | \mathcal{V}\text{ is finitely generated}\}$ is at most $\kappa$. Fix $\mathcal{V}$. Suppose $x$ is an isolated point of $D^\alpha S\mathcal{V}$ for some $\alpha$; let $\alpha_x$ be the least such $\alpha$. Choose a basic open set $N_x\subset S\mathcal{V}$ such that
$$\{x\} = D^{\alpha_x} S\mathcal{V}\cap N_x$$.
Then $N_x\neq N_y$ when $x\neq y$. Since $\mathcal{V}$ is finitely generated, the number of basic open subsets of $S\mathcal{V}$ is at most $\omega$; hence the number of $x$'s isolated in $D^\alpha S\mathcal{V}$ for some $\alpha$ is at most $\omega$. Consequently, the number of finitely generated $\mathcal{W}_{\alpha,x}^V$ adjoined to $\mathcal{U}_\delta$ to form $\mathcal{U}_{\delta+1}$ need not be more than $\kappa$.
One thing that initially gave me pause is that $\alpha$ is bounded only by $\text{card}\,S\mathcal{A}$, which could be as large as $2^{\text{card}\,\mathcal{A}}$. (For example, if $T$=DLO and $\mathcal{A}=\mathbb{Q}$, then $S\mathcal{A}$ includes types for all the Dedekind cuts.)
But then I realized that the claim "Then $N_x\neq N_y$ when $x\neq y$" holds even if $\alpha_x\neq\alpha_y$, because $D^{\alpha_x} S\mathcal{V}\supseteq D^{\alpha_y} S\mathcal{V}$ when $\alpha_x\leq\alpha_y$. Thus if we had $N_x=N_y$, we would have $D^{\alpha_x} S\mathcal{V}\cap N_x$ containing both $x$ and $y$.
When Sacks says, "the number of $x$'s isolated in $D^\alpha S\mathcal{V}$ for some $\alpha$ is at most $\omega$", he means $$\text{card}\,\{x\, |\, \exists\alpha(x\text{ is isolated in }D^\alpha S\mathcal{V})\}\leq\omega$$ Each basic open set of $S\mathcal{V}$ is determined by a formula of $T$ with parameters from $\mathcal{V}$, and one free variable. So if $\mathcal{V}$ is countable, the number of basic open sets is too, even though the Stone space might not be.
The 2nd ed. version:
Sacks modifies the definition of universal. $\mathcal{U}$ is a $\beta$-universal domain if $\mathcal{U}$ satisfies the 1st edition definition for every $\alpha<\beta$. $\mathcal{U}$ is a universal if it is $\alpha_\mathcal{U}$-universal, where $\alpha_\mathcal{U}$ is the Cantor-Bendixson rank of $\mathcal{U}$.
Proposition 31.2 and its proof, in the 2nd ed. (note that the first half of the proof is nearly the same):
Proposition 31.2. If $\mathcal{A}\in\mathcal{K}(T)$ is countable, then there exists a countable universal domain $\mathcal{U}\supset\mathcal{A}$.
Proof: Fix $\beta<\omega_1$. A countable, $\beta$-universal domain can be constructed as follows. $\mathcal{U}_0=\mathcal{A}$. $\mathcal{U} = \bigcup\{\mathcal{U}_n | n<\omega\}$ For each $\alpha<\beta$, each finitely generated $\mathcal{V}\subset\mathcal{U}_n$, and each isolated $x\in D^\alpha S\mathcal{V}$, use 31.1 to choose a $\mathcal{W}_{\alpha,x}^V$ finitely generated over $\mathcal{V}$ such that: if $x$ splits in $D^\alpha S\mathcal{W}$ for some $\mathcal{W}\in\mathcal{K}(T)$, then $x$ splits in $\mathcal{W}_{\alpha,x}^V$. Let $\mathcal{U}_{n+1}$ be a countable member of $\mathcal{K}(T)$ whose universe contains $$U_n\cup\bigcup\{\mathcal{W}_{\alpha,x}^V | \alpha, V , x\}$$.
$\beta$-unversality leads to universality as follows. There exists a countable $$L^1=L(\alpha, T, \mathcal{A})$$ such that $L^1$ is a substructure of $M$, the class of all sets; in addition $L^1$ satisfies $\Sigma_2$ replacement and every member of $L^1$ is countable in $L^1$.
Suppose $\mathcal{B}\in\mathcal{K}(T)\cap L^1$. The definition of $$S\mathcal{B}-DS\mathcal{B}$$ is a $\Pi^1_1$, hence $\Sigma_1$, recursion in $M$ that executes correctly in $L^1$ for all $\beta<\alpha_1$. As in 30.4 only countable superstructures of $\mathcal{B}$ matter, and non-isolated pre-images exist in $M$ iff they exist in $L^1$. It follows that for each $\beta<\alpha_1$, there exists a $\beta$-universal domain for $T$ in $L^1$. By Barwise compactness there exists a countable, $\alpha_1$-universal domain $\mathcal{U}$. By effective type omitting $\mathcal{U}$ can be defined so that $\omega_1^\mathcal{U}\leq\alpha_1$. ($\omega_1^\mathcal{U}$ is the least $\alpha$ such that $L(\alpha,\mathcal{U})$ satisfies replacement.) But then a result of Kreisel implies $\alpha_\mathcal{U}$, the Cantor.Bendixson rank of $\mathcal{U}$, is at most $\omega_1^\mathcal{U}$, and so $\mathcal{U}$ is a universal domain.