I love extras pages, and I love wallpapers.
Here's a comic with what may be the best extras section of any comic I read:
A lot of her extra content was made my fans, which is a great place to put that stuff (if you have any.) But I also really love her wallpapers; she's one of the few people who seems to get what makes a good wallpaper, and she makes them often enough.
I don't think you HAVE to update your extras page. Sure, you can do it every now and then, maybe once a year, maybe once every two years. But an extras section is usually only visited by new readers, in my experience. I don't regularly visit extras pages for comic I regularly read. With that in mind, you really only would want to update that page as often as your artwork noticeably changes.
And on the subject of wallpapers, personally, I love them. I have my wallpapers cycled a few times a day, and I love having a nice surprise to see what scenery graces my screen. (Right now I have screenshots from Resonance of Fate. I've never even played that game, I just thought the screenshots looked amazing.) And as someone who likes wallpapers, I love to get them for the comics I read.
And speaking from strictly personal preference, this is what I like to see from such wallpapers:
1) Have more than one available; I'd shoot for at least four, but I always want at least two good designs so I don't have the same image on both screens.
2) Avoid collages. They just look cluttered and tacky. Simple designs look really nice. People are using these on their desktops, and they may need to be able to see their icons. A cluttered image will make their clean desktop look cluttered, or a cluttered desktop will become too hard to see icons.
3) Don't have characters "looking" at the viewer. This is probably the most personal tidbit I can say, but it bugs the crap out of me when my desktop is looking back at me.
4) Have more than just pin-ups. Even if your comic does a lot of pin-up artwork, you could still have readers who don't read for your pin-up content, and don't want pin-ups on their desktop.
And it's really not hard to make a few good desktop patterns. You can take a lot straight from your comic. If you ever have a nice dramatic panel, just grab the full-sized version of it. Or take some images of just a character by his or herself, and add a simple background pattern. Or if you're working on a nice promo image to use for banner ads, make it in desktop resolutions before you crop it and add text.
All three of those ideas require little extra work over what you may already be doing.
My webcomic: Mischief in Maytia