-w and use strict; can increase your problems, but they will also definately increase your chance of finding hidden problems.
I would definately do what it takes to make use strict; happy. -w (or use warnings;) is a harder beast to keep happy and fairly often complains about things that are somewhat reasonable.
use strict; and use warnings; can always be overridden for a chunk of wierd code that you have otherwise proven is functioning correctly eg:
my $foo = 1;
my $foo = 2; #normally get a scope warning
use strict; is even better because you can override various subsets of it's checks (eg. no strict 'refs';) - see perldocs for strict and warnings