I am currently watching the third season, please avoid spoilers beyond the middle of this season (I just watched the flashback episode which make us see Olivia and Peter meet as kids).
Walter tells Broyles something like
"I would like to know what they are up to, what they are thinking..."
He speaks of Walternate and al, of course.
We previously saw the window which allowed him to see the other universe broken. Why doesn't he rebuild it ? It seems like an easy way to spy without the others knowing that they are being spied on.
EDIT : I have now watched the 5 seasons completely.
Spoiler for season 5 :
Walter spontaneously uses the window to check if the Other Side is also invaded by the Observers. So the window is still around and he remembers it.
No rational answer comes to mind for "Why didn't he think of it earlier.". Feel free to try to answer though :)