Thanks again,
during the weekend I had a chance to work on my model and truly appreciated the Cleanup plugin which helped me more than once to save the day. The above video is great too - now I know that SU layers are not "real" layers at all 
Thank you for your time.
But wait,
I've played with the above file in the lunch break. If I triple click the model, then move and delete the additional geometry and start to work with the remaining one (in group or after exploding)... the bug still persists. Exactly as described above. Any ideas?
rclub24, Gaieus, TIG,
thank you very much - stupid me!
But...maybe it should be some visual indication that parts of mode are duplicated.
Thanks anyway.
I’ve created my first model - our family house - in Sketchup 8 (running on Windows 7). The initial learning curve was really ok, after a weekend I was ready with two floors and the basement. After learning about layers I’ve placed each floor on a separate layer and start to work out the details of a particular floor while hiding the others on their layers. Then the problems begun: after showing hidden layers, planes (faces) were breaking up inexplicably into a triangle-rectangle mesh, straight lines were breaking up to segments, after the “select all” command ghost planes and lines appeared - suddenly all my effort went to fixing these issues by re-drawing pretty much the whole house.
I tried to grouped each floor separately. No help. I took attention placing each group to its poper layer. No help. I isolated the problematic places to a different file to the default layer: Layer0. No help. I’ve exported in Collada format and re-imported the file. No help. I save it in SketchUp 7 format an opened in SketchUp 7 just to get the same issues. After all of these I don’t know what else I could try.
I’m attaching a Sketup model with an example of the issue. Here you can draw a line at the missing edge to close the model. When I do this the model closes indeed (I’ve got a solid box) but then:
I can’t select (and delete) just the ceilings - the inner part of the top cover without selecting the top part of walls. Clicking on the top selects the whole top plane as one entity.
Second issue is that clicking the line I just draw reveals that it is composed of two parts (a shorter and a longer) as if it is touching some hidden entity I am unable to observe and remove.
(Sometimes - randomly - the line doesn't break up after drawing it, but then the front plane, a wall, will not close. Delete the line and try again if this happens.)
Could a Sketchup guru explain me what is going on here? Thank you for your help in advance.