/.*?([0-9]).*?\1/ *what's most interesting about this, is that $1 does not work in place of \1.

Well, of course! $1 and \1 mean different things. When $1 is used in a regex, its value is interpolated as the regex is compiled, just like any other variable. For example:

'b' =~ /(.)/;
print "Yup!\n" if 'ab' =~ /(.)$1/;
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prints Yup! because $1 holds 'b' from the first match and the second regex is compiled as /(.).*c/.

\1, on the other hand, is special regex syntax, and matches the same thing that was matched by the first capturing group in the current regex.

'b' =~ /(.)/;
print "Yup!\n" if 'ab' =~ /(.)\1/;
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does not print Yup!, because \1 wants to match an 'a'.

(\1 on the right hand side of a substitution, with the same meaning as $1, has been deprecated for quite some time.)

Update: Fixed the explanation; an earlier revision of the example used 'c' instead of 'b'.