my @subs;
{
    no strict 'refs';
    my $st = $class . '::';
    @subs = keys %$st;
}
[download]

Unfortunately, there's no way to differentiate between methods and regular subroutines, and as moritz pointed out, that won't find inherited methods which exist in different packages. Moose's metaclass facilities are really great, but naturally they only work for objects that are built with Moose.

There is Class::Inspector, which has a reasonably good function to search a class's @ISA tree and get a list of every possible inherited method.