When Modifiers Dangle--another word position vs. word reference problem

Acceptable dangling--when you can infer "who done it," "who it was," "what belonged to it," etc. (We can improve it, but it's a matter of style, not an "error.")

Having finished the assignment, Jill turned on the TV.

Unacceptable dangling--when you cannot tell "who done it" etc.  (It's an error.)

Having finished the assignment, the TV was turned on.
 

Really unacceptable dangling--when you cannot tell (etc.) and it produces comic or tragic effects in readers  (It's an entertaining error, but we still have to repair it.)

When only three years old, my mother went back to work.

On entering the room, beer was being served.