The documentation for ref (for which my code is essentially a wrapper) mentions a possible return value of LVALUE. When does this happen?

An LVALUE is something that can be assigned to (ie can appear on the left hand side of =. An easy way to see it returned from ref is by...

my $str = "hello";
print ref \substr( $str, 0, 2 );
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The docs also mention different behavior "If the referenced object has been blessed into a package". (I don't really have a question about this, other than that I don't understand it. Grokking object-oriented Perl is my next quest.)

Compare the output from these two print statements

print ref {};
print ref bless {}, "MyObject";
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How can I create a circular reference? If I do, is there a sane way to represent it?

See what Data::Dumper does with circular references? DD is usually quite sensible.

Is there a sexier way to handle code references? In particular, can I get it to print the name of the subroutine (if there is one)?

You could look at B::Deparse, which will decompile a coderef.

Update: I don't think you can get the sub's name, though

Is there a way I can use the debugger to stop at a certain point and execute my code (if, say I prefer to use it over the debugger's x command)?

Yes. If you start the program running under the debugger, $DB::single = 1 will force entry into the debugger. You can then execute any Perl code you like. (It might be DB::Single, but I'm fairly sure it's lowercase 's'.)

update: fixed a couple of typos & added deparse disclaimer