OK finally got around to typing this.

1. The Forgotten was released as an official single for the Twilight soundtrack. I think most people remove it because they think it was a ¡Tré! single, which it wasnt. Green Day announced a while back, along with Twilight, That it would be the soundtracks lead single.
2. Shoplifter has been here forever with no complaints. The one I saw recently was "Surely not Shoplifter" so they removed it based on opinion. And as for the other we had an agreement a while back to keep this one but people have started removing it again. This was a collaboration from Green Day and Husker Du. It was an "official released Split single". One side was the original version and the other Green Days version from "Warning". But either way both are sourced and the source is reliable and many other sources on this page come from this site as well. 
This one I dont see any complaints about. It never had a war to remove and only was reverted a while back. Various other ones have this section and its not that long. So it doesnt make the page to huge and not every discography "has to have one". I dont think that this is a problem and it really does make the article more complete. The only thing missing is demos if we want to add them.

 So this is what I think and what do you say about adding demos. Its not to many and wouldnt be a problem with sources and what not.
I also think we should add Cigarettes and Valentines to the studio albums page and put "Unreleased" I added it once but one person didnt like it and kept reverting it.