davidrw answered what $/ is, the input record separator. I just used it to print the newline. I most likely wouldn't want the newline if I were assigning the sheet name to a variable.
Since $/ defaults to "\n", I use it in one-liners so I don't have to think about shell quoting issues (I use both Win32's cmd and bash regularly), and it looks like it's crept into my test scripts too. I would not use it as a newline in production code.
About the warning, my $current_sheet = $sheet->Name, $/ is parsed as
((my $current_sheet = $sheet->Name), $/);
The comma operator in scalar context evaluates the left side, throws it away and returns the right side, a bare "$/". Look in
perldiag for "Useless use of %s in void context".