Not sure I understand the point of this card. By itself, it costs 6 clicks and 2 credits to be worth an agenda point.

Seems like you would be better served by pretty much any other Agenda. 

From what I know of the game:

Pros: Food for Archer, no-point bait for Midseason Replacements / Aggressive Negotiations (both out of faction though), lets you get that last point after three 2-pointers, where you'd normally be scrambling for another 2-pointer, worth nothing if the runner steals.

Cons: Bait for Data Dealers, requires a full turn to actually score the point.

That said; this makes click-gaining cards seem more appealing (Mandatory Upgrades, Director Haas, Haas-Arcology AI), as they'd give more breathing room for actually scoring this.

I haven't looked into the new cards too much, but that's my analysis regarding existing cards.

It's an agenda that is worth nothing to your opponent (unless they have Data Dealer, ect.) while potentially being worth the game-winning point for yourself. That alone is pretty special. Furthermore, it is HB's only 2-cost agenda, meaning you can play it and score it in the same turn without any extra clicks or other ways for pushing an agenda out faster than normal. In the faction that is masters at getting extra clicks. But you might think "what's the point of a fast-scoring agenda if you have to spend 3 extra clicks to make it worth something?" Well, things like Archer are one reason. But also, it just get's it out of the way, safe from ever being stolen - you can activate it's ability at your leisure. No need to rush those 3 clicks until you actually are at the winning break-point. It potentially tricks things like Logos and Iain Sterling with the pseudo victory points. Lastly, who knows what the future may hold? Maybe there is a nice card in the future that spends agenda counters on your agendas for something awesome, and Domestic Sleepers would give you a renewable source of agenda counters. Who knows?

Can you utilize the ability more than once? It looks like you could just click your way to 7 agenda points unless there's a reason you can only put one counter on it.

"[Click], [Click], [Click]: Place 1 agenda counter on Domestic Sleepers.
Domestic Sleepers is worth 1 agenda point while it has at least 1 agenda counter on it."

NM I just caught it... It's only worth 1 agenda point no matter how many counters over 1 are on it.

They all laughed at me when I said there should be 0-point agendas.  Well who's laughing now?  HAHAHA!  I guess it's me. 

NM I just caught it... It's only worth 1 agenda point no matter how many counters over 1 are on it.

Pros: Install, do not necessarily advance. Runner would spend a click - and maybe credits - to access a 0-pointer.

Cons: Eats slots in deck building, since you are committed to agenda points, and this one is worth 0. So, as it is illegal to replace 2/1 or 3/1 agenda with this, you have to play it in addition to your set of agendas.

Put it into a server and advance it two times. The runner may spend his whole turn and/or his credit pool to break into the server, only to find a 0 point agenda. If he doesn't run, score and feed it to Archer/Enforcer 1.0/Corporate Town. It also triggers "when an agenda is scored" effects, like one of the new HB assets in The Universe of Tomorrow (Team Sponsorship), and shuts down the runner's current. And if you're in late game and need only one/two additional point(s) to win, pump it/them up.

All of that without the risk of losing points to the runner. Very versatile. The only downside is that it needs deck space. Oh, and it's vulnerable to Turntable. So you might include some Hardware trashing. Like Enforcer 1.0... oh, wait - that's likely already part of your deck.

The uses for this one have already been discussed quite well. Just to sort a couple of things.

You CAN use the agenda counters to feed Mark Yale. How stupid and pointless it is to convert three clicks into three credits with an additional card is another topic. If you are planning on overadvancing Vitruvius and include stuff like Project Wotan one might gain a couple of credits. Anyway...

I don't look on this as an agenda the Runner can steal. I mean, he must, but he gets no points, while the only real threat there is Turntable, which is meta-dependant for now. Still, Turntable is a threat to every agenda out there, so not much of a concern here.

Great with Utopia Fragment for obvious reasons. Add in 1 or 2 Aggressive Negotiations for the safest card search there is - install under ice and use your two clicks for something else. Next turn score and fetch a card. Even if it fails, you don't lose too much. Also nice with Efficiency Comitee - score a couple Domestic Sleepers from hand, fast advance EC. Now when you get to 5 points, burn the EC counters and your turn to generate 2 agenda points for the win. Thus without giving points you are playing to reach 5, not 7. Once in a million maybe, but still possible.