I like this approach! To extend the idea even further, if the phrases are short and there is a small number of mismatch types, each item could be reduced to several canonical forms, and those could be used as keys to the hash. For example, cat could be reduced to ca?, c?t, and ?at, to cover single-letter substitutions. So cat is found in that hash as a value in three different buckets. Faced with the word hat, one of its canonical forms, ?at also keys into a bucket containing cat and gets added there.

Other canonical forms might be obtained from Text::Soundex or Text::Metaphone where "similar" means "sound alike".

How to then transform this hash of word affinities into a single list with no repeats is left as an exercize for the reader. :-)

Update:

To flesh out the soundex idea a little, here's a short example:

use strict;
use Text::Soundex;
my @inwords = qw(holly perl monks yahoo monk holey google eperl holy g
+oxgle kugel april);
my (%hash, @outwords);
push @{$hash{soundex($_)}}, $_ foreach @inwords;
push @outwords, @{$hash{$_}} foreach keys %hash;
print join(' ', @outwords);
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It prints:

google goxgle kugel perl holly holey holy yahoo april monks monk eperl
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Since each word in this example has but one canonical form, it appears in the hash exactly once. So there are no repeats to untangle as with the cat/hat illustration.