cp -r {*,.??*} /dest && rm -rf
Copies (cp) all files within the current directory (*) (including hidden files beginning with '.' but with at least two characters if its hidden '.??*' prevents traversing up to higher level directories) recursively (-r) to the folder '/dest' once thats complete (&&) then remove (rm) all files/folders recursively (-r) and without asking (f).
If you're mp3's are messy and not tagged correctly, but in structured folders then before moving them you could consider using something like
EasyTag which will attempt to tag them appropriately.