... the next lines do not compile: ...

I've played around with this some more and I'm coming to the conclusion that this has little or nothing to do with Regexp::Common::delimited and more to do with the use of a regex delimiter character within the regex pattern. The following works as I expect with any of
    '\/'  '\\/'  '\\\/'  '\\\\/'  '\\\\\/'  '\\\\\\/'
as the  -delim delimiter specification:

c:\@Work\Perl\monks\Veltro>perl -wMstrict -le
"use Regexp::Common qw(delimited);
 ;;
 for my $s (qw(
   a/b/c  a\b\c  /a/  \a\  a//b  a\\\\b  //  \\\\
   a/b  a\b  a/b\c  a\b/c  a/  /a  a\  \a  /  \
   )) {
   print qq{'$s' },
     $s =~ m{$RE{delimited}{ -delim => '\/' }} ? '' : 'NO ', ' match';
   }
"
'a/b/c'  match
'a\b\c'  match
'/a/'  match
'\a\'  match
'a//b'  match
'a\\b'  match
'//'  match
'\\'  match
'a/b' NO  match
'a\b' NO  match
'a/b\c' NO  match
'a\b/c' NO  match
'a/' NO  match
'/a' NO  match
'a\' NO  match
'\a' NO  match
'/' NO  match
'\' NO  match
[download]

Both  m: ... : and the balanced  m{ ... } (my personal preference per TheDamian's regex PBPs) yield the same results.

For a  / ... / delimited match with the code above, the  -delim strings:

• '\\\/'  '\\\\\/' work as expected;
• '\\/'  '\\\\/'  '\\\\\\/' fail to compile (Can't find string terminator "'" ...); and
• '\/' works partially as expected (go figure).

Again, the lesson seems to be: be wary of the presence of a delimiter character within a regex pattern.

IIRC from previous regex compilation discussions (and please don't ask me for a citation :), I think what's happening here is that the regex parser looks for the end of a regex using various heuristics as soon as it sees that a regex has opened, and in this case, it sees the forward-slash at the end of the first  '\\/' (or whatever) single-quoted string and sometimes mistakes it for the regex terminal delimiter. The Perl parser looks for single-quoted strings thereafter, and goes off the rails when it sees that a final single-quote is unmatched. Or something like that... Anyway, don't use  // regex delimiters here.

Update: The "premature regex termination detection" theory is supported if the
    my $rx = qr{ $RE{'\\\\/'} $RE{'\\\/'} $RE{'\\/'} $RE{'\/'} $RE{'/'} };
regex from Re^3: Delimiters in Regexp::Common (updated) is re-written with  qr/ ... / instead: the "Can't find string terminator "'" anywhere ..." compilation error results.