In the final episode of the first season of Fringe, Walter has gone missing with the Observer, and Nina Sharp has been shot by Robert Jones. Now suffering the full effects of teleporting, Jones is forced to speed up his plans to kill William Bell, and so he shoots Nina Sharp to get the fuel cell out of her robotic arm so that he can bridge the gap between our dimension and the one that Bell is currently hiding in. The Observer instructs Walter to search an old beach house he used to own for an item which will help stop Jones from accomplishing this goal. Peter joins his father in the hunt for the item, and together they discover that it is a means of closing the bridge between the dimensions. As Jones begins to cross the barriers between the two dimensions, Peter arrives with the device which closes the portal on Jones, leaving half of his body on either side. With the day saved again, Nina Sharp promises a meeting with Bell. However, after waiting an hour for the meeting to begin, Olivia leaves, angry at Nina for going back on her word. As she exits the elevator, she steps through a portal to the alternate dimension where Bell is hiding and finally gets her meeting. Walter visits a grave marked "Peter Bishop", which explains to the watcher that the Peter of this dimension died and Walter retrieved another one from another dimension to replace him. Which leaves the question, what about the alternate Walter? What happened to him?
Anyway, the Observer is again key in the plot of this story, so you can't miss him. First he is watching Walter look at Peter's grave. Then he is trying to remind Walter about what he needs to find in order to stop Jones, and also hints that, "There is more than one of everything." which we discover later to be a reference to Peter being not of THIS earth. Both pictures are below with the Observer in a red box, but you really shouldn't need it.