If you use warnings, you should get a warning message like:

readline() on unopened filehandle at ...
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Also, if you use diagnostics, you should get a little more help on that message:

readline() on unopened filehandle at ... (#1)
    (W unopened) An I/O operation was attempted on a filehandle that w
+as
    never initialized.  You need to do an open(), a sysopen(), or a so
+cket()
    call, or call a constructor from the FileHandle package.
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Well, those might not be the most helpful messages to you, but at least they give you an idea that something is amiss. To avoid the voodoo of <>, use glob:

use warnings;
use strict;

my $path = '/var/log/*';
my @files = grep { -f } glob $path;
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See also:

• use strict and warnings
• Basic debugging checklist