"Note that splitting an EXPR that evaluates to the empty string always returns the empty list, regardless of the LIMIT specified."

$rem holds an empty string, so an empty list is assigned to ($middle, $last), setting $middle and $last to undef.

Fix:

use strict;
use warnings;

use List::Util qw( shuffle );

while (<DATA>) {
    s/(?<=\w)(\w+)(?=\w)/ join('', shuffle($1=~m{.}sg)) /eg;
    print;
}

__DATA__
I couldn't believe that I was actually understanding what I was
reading. The phenomenal power of the human mind, according to
research at Cambridge University, suggests that it doesn't matter
in what order the letters in a word are, as long as the first and
last letters are in the right place. The rest can be a total mess,
and you can still read it without a problem. This is because the
human mind does not read every letter by itself, but the word as
a whole. Amazing, huh? Yeah, and I always thought spelling was
important! Check apostrophe and punctuation: Jame's, They're,
we'll they'd.
[download]

By the way, try replacing

shuffle($1=~m{.}sg)
[download]

with

sort $1=~m{.}sg
[download]

It'll probably be harder to read.