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Yes after doing complicated things like invoking a subroutine $_ is pretty unsafe. ¹)
Not only subs, there are plenty of commands which have a side effect on $_.
$_ is only a shortcut with limited use in small situations that you can completely control, but over time code grows in unexpected ways.
Better use named lexical variables in production code, especially when it is maintained by various people. ²)
Global variables are generally more critical and should only be use for good reasons.
I can strongly recommend you getting a copy of Perl Best Practices for good discussions of such issues. It will certainly improve your Perl skills.
¹) for completeness you could use local $_ (or even my $_ in recent Perls) within the subroutine, but this doesn't really solve the general problem of $_'s limited radius.
²) Think of $_ as the word it in human language, the longer a conversation only using "it", the unclearer what it (sic) is supposed to mean.