Funny, I was just wondering the same thing. It seems as though it was supposed to mean something, but I have no idea what. Clearly there is a painting missing there.
Whoever posted this question 4 years ago probably won't see this, but I thought I'd contribute.
I've seen things that would make you want to write a book on how to puke.

symbol of some thing missing
some thing wrong
how slow things change
in that House
of Yes/no+no=oui
rats doivent laver les pattes
vor der Ruckkehr in die Kanalisation

As partridgestorm pointed out (here and in another thread), it's Edouard Manet's The Railway, a painting of a woman and child beside a fence. The woman is looking up from reading a book and has a dog in her lap, while the girl is looking through the bars at passing trains. You can see it around the third minute into the movie, when the kids are doing their faux tour.
http://www.independent.co.uk/arts-entertainment/art/great-works/manet-edouard-the-railway-1873-810754.html
I think it's a subtle prison reference: Jackie-O, locked up in the house, watching soap operas and the Kennedys through the windows and her father leaving and Marty leaving her behind with her mother and the obedient but dumb Anthony.
As for why it's not there in the present day, I think it's meant to symbolize everyone in the house knowing the truth but not admitting/facing itthat the house is a gilded cage for all of its inhabitants, most notably Marty, who only thinks he's found an escape. Leslie picking at the discolored wallpaper draws attention to it, the way her presence draws attention to the wrongness of the family dynamics.
It's also nicely referenced with Mrs. Pascal's offers to have a cab take Leslie to the train station. She can leave anytime.
In less symbolic terms, with the talk of the last shooting staining the carpet ("There's still a shadow"), I wonder if the painting wasn't somehow damaged when Jackie-O first shot Marty.

I think it's the spot where Royal used to hang his Javelina. : )
Seriously, I have no idea, but I just re-watched "House of Yes" tonight and dug ti all over again, man. Super!

the blood splatter from shooting the father ended up, so they had to remove the paintings
Possibly. But the problem with that idea is that there'd be blood on the wallpaper near the painting and they have to scrub the walls to clean them. But we can clearly see a dirty outline of the missing painting.
What Would Jesus Do For A Klondike Bar (WWJDFAKB)?

i thought it was supp to be a picture of there father
you have to ask yourself are you a fighter, or are you zombie food

it's where the blood splatter from shooting the father ended up, so they had to remove the paintings
i'm having the best time!

Do you still have the movie? I just watched it yesterday, and I'm pretty certain that it is Manet's "The Railway." If you look closely at the scene, the figure on the right is wearing dark colors and the figure on the right is wearing white with blue in the center. I just posted about this yesterday, and I'm looking to see if anyone else sees what I see.

When I watch the opening sequence where young Jackie starts to run around all crazy in that room, I think I see that it's a picture of the twins next sitting next to each other as babies.

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I'm not sure but does it have anything to do with their murdered father? That's a good question - I'm going to watch it again.

About 30 minutes in, when jackie asks leslie about her being poor, exactly after she asks if they even have paintings in pensylvania. I didn't get it either, maybe someone does. Hope this helps.

When does that happen?
)
..) .*)
(. (.