But Hulu Plus can’t show subscribers all of the episodes of all the shows in Hulu’s catalog. Rights issues mean that certain shows will flit on and off the service, and it’s up to subscribers to figure that out for themselves.

Example: “Modern Family,” ABC’s award-winning hit sitcom, disappeared from both Hulu and Hulu Plus this summer after its first season. Now it’s back. But both services are only offering shows from the current season–there’s no way to go back and catch up on last year’s shows, even if you’re paying.

I think, but haven’t been able to confirm, that this has to do with DVD sales for the show, which is produced by News Corp.’s (NWS) 20th Century Fox. I’ve got queries into both Fox and Disney’s (DIS) ABC to try to confirm.

Meantime, here’s what Hulu has to say:

Yes, the first season of Modern Family is no longer on Hulu Plus. We acknowledge this can sometimes be confusing for TV fans, so we do all we can to provide as much advance notice as possible when shows are slated to come down. Below is an example from our Saturday Night Live show page on Hulu Plus. You’ll notice it says “New episodes are posted Sunday afternoons and are available for 17 days.” This is consistent across all our content.

Of course, we keep content on Hulu and Hulu Plus for as long as possible. We can’t offer a specific reasons why a particular video may be taken down, as streaming clearances differ from show to show.

And sure enough, if you head to each show’s Hulu page, you’ll find a different set of availabilities.

Regular Hulu users can only see the last five episodes of “The Family Guy,” for instance, while Hulu Plus subscribers can see all nine seasons. But even if you’re a paying customer, Hulu can only show you five episodes of “The Simpsons,” period.

Meanwhile, the last season of “Lost” fell off both the free and paid services last month, and the other five seasons will go away at the end of the year. Etc.

To be fair to Hulu, it’s certainly not the only service negotiating the frustrating rights/windows patchwork. Everyone who deals with digital media has to navigate this stuff. And none of it makes sense to viewers who just want to watch their shows, when they want to watch them.

But the patchwork is a bigger deal for Hulu, because the service’s primary pitch is that it’s a one-stop shop for all your TV viewing (or at least your broadcast TV viewing). Instead it’s really closer to a half-stocked Super Target: There’s a lot of stuff in there, but you still may not find what you need.

Hulu competitor Netflix (NFLX) offers lots of TV shows via its paid streaming service, too. But it pointedly doesn’t play up the presence of any particular show–Reed Hastings and company simply tell consumers that they’ll find shows they like.

But if you’ve ponied up $10 a month for Hulu Plus and find that you still can’t watch a show that aired a few months ago, you may not be cool with that at all.

Gaps in Hulu’s free service may not be as frustrating for users, because they’re not out any cash. But it is a problem for the joint venture as it ponders a public offering, premised on the notion that its TV partners/owners–ABC, Fox and GE/Comcast’s NBC–are in it for the long haul.

But if Hulu can’t tell users that it has all the rights it needs, how can it convince investors?

Meanwhile, a similarly confusing story:

The network is the only one of the four broadcasters offering much programming on Apple’s device at launch Saturday. As previously reported, the Disney (DIS) unit is offering about 20 of its shows, including “Lost” and “Grey’s Anatomy,” for free via a new app.

But that’s about it. Come Saturday, CBS (CBS) will only be streaming full episodes of “Survivor” at its iPad-friendly site. And News Corp.’s (NWS) Fox and GE’s (GE) NBC aren’t streaming any full-length shows at all. If you want to watch “CSI,” “The Simpsons” or “30 Rock” on your Web browser this weekend, you’ll need to use something other than an iPad.

CBS says it will offer more shows over time, but NBC and Fox aren’t even promising that. When the Hulu app arrives, those two networks’ shows will be available there, but under current plans, they’ll be available only to paying subscribers.

The holdouts’ logic is that the iPad is a mobile device. And while the networks are basically okay with streaming their stuff for free on the Web, they think that mobile is a different ballgame, and one they can charge for (though even that’s confusing — NBC does stream full-length shows for free to the iPhone, but won’t do the same for the iPad).

But if that’s the reasoning, why is ABC, which joined up with Hulu a year ago, putting up its stuff for free on the iPad? The fact that Apple (AAPL) boss Steve Jobs is Disney’s largest single shareholder can’t be the only reason.

ABC may be able to thread the needle here because it is only making its shows available via Wi-Fi streaming, not over AT&T’s (T) network. But that kind of “windowing” is going to seem awfully arbitrary to most casual users, and those are the ones both Apple and the networks are supposed to be targeting here. So something’s going to have to give. Stay tuned.