See the second half of this video for a demonstration/explanation:
https://youtu.be/tLeW3lhMn_0

The behavior of Observers in regard to their opacity is inconsistent. (I am referring to their functional opacity - whether or not they cut off redstone wire, can they have torches placed on their sides, etc., NOT their visual opacity.) You may expect them to act like opaque blocks, and they DO cut off redstone wire, but in every other aspect they act like upside-down slabs/stairs, in that they act like transparent blocks, with the exception of being able to place redstone/buttons/levers/etc. on their top side, but not any other sides.

I didn't realize it when I made the video, but making Observers opaque would cause them to be able to weakly power adjacent blocks, which would interfere with their functionality and make them a lot less useful in my opinion. Therefore, I think the best way to resolve this would be to make them act like slabs/stairs. So basically, they would act just like they do now, but would not cut off redstone wire.

However, if the devs decide that Observers, due to being rather unique, belong to their own unique set of opacity rules, then I think Observers should act like opaque blocks (levers/torches could be placed on their side), minus the ability to be strongly powered, so as to prevent them from transferring redstone signals to any adjacent blocks and interfering with their functionality. This would actually make them just like MCPE pistons currently are in regard to how they behave when it comes to being transparent or opaque. Perhaps they could be in their own new category of blocks that are transparent except they can have blocks attached to any of their sides (rather than only their top sides like slabs/stairs) and they also cut off redstone. Maybe they would be considered opaque, but non-redstone-conductive? Not entirely sure what the terminology would be.

As of 16w44a, observers in the Java edition act like any other transparent block in that edition: you can't attach stuff on its sides and it doesn't cut off redstone wire.