K.S.
Hi-
Been there with the whole nasty grimy tub! I have found what works best is scrubbing bubbles brand shower scum remover, its at safeway in a spray bottle and it works miracles! spray it on, leave it a few minutes to soak the grime off and come back and sometimes you need to scrub it off but most of the time it washes off. About the mini blinds......usually you soak them in hot soapy water, but if you have white ones you can add bleach with the soap and water.....i did this and they looked BRAND NEW!!
GOOD LUCK and HAPPY CLEANING!!!
K.