Who needs RCS iterations? According to this paper of Chaz Schlindwein, any countable support iteration of semi-proper forcings is semi-proper.  This seems like a breakthrough simplification, and I wonder why it is not more well-known.  Before diving into the arguments I want to ask the forcing community whether this work is widely viewed as correct?  Thanks for your help.
 A: I think that this claim is false, at least in the way that I understand "countable support".  The following  was explained to me by Menachem  Magidor in the 1990s; it may be folklore, and I suspect it is the reason for introducing RCS in the first place.) 
Consider the following countable support iteration $(P_\alpha, Q_\alpha: \alpha < \kappa)$ of length $\kappa$, where $\kappa$ is either a measurable cardinal or $\omega_2$ in a universe where Namba forcing is semiproper: 


*

*$Q_0$ is Prikry forcing on $\kappa$, or Namba forcing.  

*For each $\alpha>0$, $Q_\alpha$ is an antichain on $\omega_1^V$ (with an additional largest element $1_\alpha$ thrown in). (Really: the canonical $P_\alpha$-name for this set.) 

*Each $Q_\alpha$ is semiproper. (Even proper, except for $Q_0$.)

*For $0\le \alpha\le \kappa$, $P_\alpha$ is defined in the usual way, as the set of all countable partial functions $p$ with domain $\subseteq \alpha$ such that for all $\beta\in dom(p)$ we have $p\restriction \beta$
is in $P_\beta$ and forces $p(\beta)\in Q_\beta$. 


Then the following statements are true: 


*

*Every condition in $P_\kappa$ has bounded domain. (This would not be true if we had used revised countable support iteration.) 

*$Q_0$ introduces a new sequence $(\kappa_n: n \in \omega)$ which is cofinal in $\kappa$. (I.e., there is a $Q_0$-name for such a sequence.  Hence there is also a $P_\kappa$-name for such a sequence.) 


We define functions $g$ and $h$ as follows: 


*

*Let $g$ be a $P_\kappa$-name for the function from $\kappa\setminus  \{0\}$ to $\omega_1^V$ which assigns to each ordinal $\alpha$ the generic element of the antichain $Q_\alpha$. 

*Let $h$ be the $P_\kappa$-name for the function $n\mapsto g(\kappa_n)$. 


Then the empty condition forces that $h$ is a surjective function from $\omega$ onto $\omega_1$.  (Hence $P_\kappa$ is not semiproper.)
Proof:  Assume that $\gamma< \kappa$, and that $p\in P_\kappa$ is a condition.  It is enough to find a stronger condition  forcing that $\gamma$ is in the range of $h$.  
First find $\alpha$ such that $p\in P_\alpha$.
Note that $p$ "knows nothing" about the values of $g$ above $\alpha$, and that $p$ knows very little about the sequence $(\kappa_n:n\in\omega)$. 
Let $n$ be the length of the stem of $p(0)$, the $Q_0$-component  of $p$. By extending the stem, we can find  $p'(0)$  stronger than $p(0)$, such that $p'(0)$ forces a value (say $\beta$) to $\alpha_n$, and such that $\beta> \alpha$.  
Define $p'$ as follows:  $dom(p')=dom(p)\cup \{\beta\}$.  $p'(\beta)=\gamma$.  (And $p'(i)=p(i)$ for all $i\not=0,\beta$.) 
Now $p'$ forces that $h(n)=g(\alpha_n)=g(\beta)=\gamma$. QED

In defense of Schlindwein's paper I should add that he might have had a different (nonequivalent) definition of "CS iteration" in mind. 
A: Following up on Martin's answer:
Definition 10 of the paper defines the concept "hemi-properness", shows that semi-proper forcings are hemi-proper, and then claims (Theorem 16) that hemi-properness is preserved under countable support iterations.  This last is demonstrably false, as we will show that "hemi-properness" is equivalent to "preserves $\omega_1$", and it is well known that this property is not preserved by countable support iteration.
Definition [Definition 10 from the paper]
A poset $P$ is hemi-proper if and only whenever $\lambda$ is a sufficiently large regular cardinal, $M$ and $N$ are countably elementary submodels of $H(\lambda)$, $P\in M\in N$, and $q\in P\cap M$, then 
$q\nVdash``\omega_1\cap M[G_P]>\omega_1\cap N$''.
Lemma 11 in his paper shows that hemi-proper forcings do not collapse $\omega_1$.
Claim:  If forcing with $P$ preserves $\omega_1$, then $P$ is hemi-proper.
Let $\lambda$, $M$, $N$, and $q$ be given.  Any condition forces that $M[G_P]$ is countable (it is just the interpretations of the countably many $P$-names living in $M$).  In particular, any condition forces that $M[G_P]\cap\omega_1$ is an ordinal $\alpha<\omega_1$ since $\omega_1$ is preserved.  The model $N$ can see $M$, and so $N$ will contain a name $\dot\alpha$ for the countable ordinal $M[G_P]\cap\omega_1$ from $M[G_P]$. In $N$, we can extend $q$ to a condition $r$ deciding a particular value $\alpha$ for $\dot\alpha$.  Notice that since $r$ and $\dot\alpha$ are in $N$, the countable ordinal $\alpha$ is in $N$ as well.  Necessarily we have $\alpha<N\cap\omega_1$.  Since $r$ extends $q$, it follows that $q$ did not force $\omega_1\cap M[G_P]$ to be greater than $N\cap \omega_1$.  This establishes that $P$ is hemi-proper.
Schlindwein lectured on this at a few meetings in the 1990s. The paragraph at the top of page 9 was added in an attempt to meet my objections that his notion was the same as "preserves $\omega_1$'', but there are no such $M$ and $N$ as he describes there.
Chaz was a nice guy. I'm sad to hear the news that he has passed away.
