The nicer approach with a ternary:

my @part = (
    'http://example.net/app',
    ( 'admin'          ? $is_admin_link : () ),
    ( defined $subsite ? $subsite       : () ),
    $mode,
    ( defined $id      ? $id            : () ),
    ( defined $submode ? $submode       : () ),
);

my $uri = join '/', @part;
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Said all this, probably I wouldn't have thought of the boolean list squash operator. I would have tried to "encapsulate" the component data and map it through some suitable code. Of course the problem is: which code? Of course, the answer is that there are tons of ways that work, but I also want something which is visually clear at a glance, and unobtrosive. I considered some possibilities involving nested ternaries which would e.g. distinguish refs from non-refs, and then arrayrefs with two elements from ones with one. Then I considered as an alternative chained map()s achieving the same effect for clarity at the expense of multiple looping where a single one would suffice. But then I wouldn't want two or three "header" lines of code only to suck up say other six. I really want at most one, and simple enough. Eventually, the best alternative I could think of is:

my @part = map defined $_->[-1] ? $_->[0] : (), 
  ['http://example.net/app' => 1],
  ['admin' => $is_admin_link],
  [$subsite], [$mode => 1], [$id], [$submode];
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Here:

1. the additional visual "encapsulation" given by square parens allowed me to put several params on one line with no risk of confusing them;
2. I forced a => 1 on elements that you were originally unconditionally inserting: since these were supposedly true, it's completely useless but possibly as a visual reminder that they are, and in turn this is silly for the constant item but may be sensible for $mode.

As a sort of counter-example, if I wanted the unconditionally inserted elements to be included in the list without the burden of the square parens, then it's obvious how to do it:

my @part = map +(ref) ? (defined $_->[-1] ? $_->[0] : ()) : $_, 
  'http://example.net/app',
  ['admin' => $is_admin_link],
  [$subsite], $mode, [$id], [$submode];
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Here, the first line is getting long and confusing, and the absence of square parens around $mode also degrades readability.