You can simplify your code considerably by using the DBI "fetchrow_hashref" function (which gets each row as a reference containing the column names as keys and the column values as values) instead of storing the column data to separate parallel arrays. Something like this:

my $sth = $dbh->prepare(  "SELECT pmid, abstract FROM PM_text "
                        . "WHERE title LIKE '%E.coli%'"        );
$sth->execute;

my @text_refs = ($sth->fetchrow_hashref());

$sth->finish;

...

for my $text_ref (@text_refs) {
    for my $cont_name (@cont_names) {
        if ($text_ref->{abstract} =~ m/$cont_name/im) {
            for my $bact_name (@bact_names) {
                if ($text_ref->{abstract} =~ m/$bact_name/im) {
                    print  "matched at text $text_ref->{pmid}, "
                         . "for $cont_name and $bact_name\n";

                    $sth2->execute( $bact_name,
                                    $cont_name,
                                    $text_ref->{pmid} );

                    $sth3->execute( $cont_name,
                                    $text_ref->{pmid} );
                }                          
            }                              
        }
    }
}
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Possibly you have a logic error here - the "$sth3->execute()" call depends only on the outer two loops, but it is occurring in the innermost loop. Thus if more than one bacteria name matches for a given abstract/contaminant pair, you will end up trying to insert duplicate records into that "PM_cont" table. Possibly the "$sth3->execute()" call should be moved out one level.