"... anyone who names their package "0" is going to asking for trouble!"

Naming a package 0 is a fatal, compilation error:

$ perl -e 'package X;'

$ perl -e 'package 0;'
syntax error at -e line 1, near "package 0;"
Execution of -e aborted due to compilation errors.
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The problem is likely to occur where, in some code completely separate from yours, someone writes '$x->your_method()' when, perhaps, '$y->your_method()' was intended.

I had some difficulty coming up with an example. Here's some valid, albeit highly contrived, code to demonstrate the concept.

$ alias perle
alias perle='perl -Mstrict -Mwarnings -Mautodie=:all -MCarp::Always -E
+'
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$ perle '
    package X {
        use Scalar::Util "blessed";
        sub new { bless {}, __PACKAGE__; }
        sub meth1 { say "meth1: [", ref $_[0], "]" }
        sub meth2 { say "meth2: [", blessed $_[0] // "undef", "]" }
        sub meth3 { say "meth3: [", defined blessed $_[0], "]" }
    };

    package main;

    my $x = 0;
    my $y = X::->new();

    $x->X::meth1();
    $x->X::meth2();
    $x->X::meth3();

    $y->X::meth1();
    $y->X::meth2();
    $y->X::meth3();
'
meth1: []
meth2: [undef]
meth3: []
meth1: [X]
meth2: [X]
meth3: [1]
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The 'package X;' is intended to represent your code; the 'package main;' (although quite superfluous here) is intended to represent "some code completely separate from yours".