It seem to me that the dome represented Peter's isolation from the rest of the group. As if he was in a world of his own. I even theorized he created his own universe of which he was the population of one until he could find his way back to join his friends. See that post here.
Even in the third season of Fringe the dome was part of episode 20, "6:02 AM EST as pictured below.
The Geodesic dome has once more made an appearance on Fringe and this time it was in the the most recent episode, "Subject 9". It was very subtle and much less obvious. But it was in relation to Peter's return and situated with the one person who may hold the key to Peter's re-intergration with the new timeline, Walter. Here is the picture.
This time the Geodesic dome is shown in miniature form as it sits on the work table directly in front of Walter. To read more about Bucky Balls and Geodesic domes follow the link here.
The Dome or Bucky Ball may well become a constant theme for the entire season. It could represent isolation, pocket Earths, existential crises, bubble universes or anything that sets Peter and the group apart. It could also mean there is more than one of everything, you just have to know where to look!