It probably means an unrealized or unrealistic dream (dream as in goal, not the sleepy kind of dream), but like Hilary said, it's hard to tell without knowing the context.

No idea - please provide context.

This is poetry, or from a song, right? When you misplace something it usually means you can't remember where you put it - I frequently misplace my spectacles. It can also mean that you put it in the wrong place, again making it hard to find. Probably the writer has misplaced a dream and can't find it - this makes sense, we often forget our dreams when we wake up, and wonder how to recover them. Alternatively the writer has found somebody else's dream wherever that person left it; this could be very annoying. For example if somebody dreamt that your train had been cancelled, you could be late for work.

I suspect it is most frequently used as in "misplaced trust". This is when someone or something is/was trusted, but should not have been for some reason. I suspect "misplaced dream" as Joe says means a dream, a wishful thought, an intended goal, a long-hoped outcome, was unrealistic for some reason. . His long-time dream was to one day be rich beyond compare. Given that he had no talent for anything useful, it was a misplaced dream. Better example, anyone?