The perspex covers on my Beolab 3000s were both loose when I got the speakers (the double sided foam tape had long since rotted and so the adhesive parts had seperated and were stuck the perspex cover and amp body respectively). I have not bothered to restick the covers because when I came to look at them the inside window of the cover (where the display is visible) was thick with a type of black dust. I guess this is some sort of carbon dust stuck there by static, because of the electrics of the amp? Anyway it was so dirty that it was reducing the visibilty of the display ( the front of the display also had a similar buildup, which I, VERY CAREFULLY, wiped off). Anyway, long story short (too late lol), I decided not to stick the covers back on because they seem to stay in place ok on their own, and if I need to clean inside again it can be done reasonably easily.
BTW I have been told that one of the best products for removing fine scatches from plastic is Brasso, but don't just attack your treasured speakers with it on my suggestion, test it first! (I haven't tried it yet).