I use my phone to see my pm's mostly, check adds if i'm bored, and read the newest posts. I've never used the search on my phone, or just read old posts for the hell of it.
Having a go to full site button would be useful if located as one of the first things to load. I find it difficult now to select the "view unread posts" or "view new posts" part. And in reading pm's you only get to see the pm and part of the quoted ones. You can't scroll to see the whole history of the pm on a phone now.
Someday someone may kill you with your own gun, but they should have to beat you to death with it because it is empty