You've flagged the wrong line as giving the error:

c:\test>junk
Invalid value for shared scalar at c:\test\junk.pl line 8.
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The line with the problem is $foo{'bar'} = [$i, $j, $k];

Not $foo{'bar'} = &share([]); #<-- Not what it wants this one.

The problem is that having successfully assigned an anonymous array (reference) to $foo{bar} by disabling the problematic protoype using &share( [] );, you then try to assign a new, completely different anonymous hash reference to it.

Instead of this $foo{'bar'} = [$i, $j, $k]; which (unsuccessfully) attempts to overwrite the shared anonymous hash with a different non-shared anonymous hash with three values in it, you should assign the values through the shared reference like this

@{ $foo{'bar'} } = ( $i, $j, $k );
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With that change, your snippet produces

c:\test>junk
$foo = {
         'bar' => [
                    #0
                    '1',
                    #1
                    '2',
                    #2
                    '3'
                  ]
       };
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You may find Re: Using threads::shared with multidimensional arrays helpful.