German Mist means "dung" - I had assumed the similarity to English mist was a coincidence, but it isn't. They are both from Proto-Germanic *mih-stu- "urine", and the English word took an unexpected semantic turn.
The Proto-Indo-European root is *h₃meiǵʰ- "to urinate".
The Proto-Germanic diminutive *mihst-ila- referred to mistletoe, which is propogated thru the droppings of the missel thrush. This became Old English mistel, which combined with tān "twig" to form misteltān. The tān was reanalyzed as being the plural of tā "toe", and the word changed to mistelto then mistletoe.
I'd better add that the ODEE has a different derivation: PIE *meigh- "to glimmer, twinkle; mist". Not sure how the German word fits in.