The finishes should match for each distinct space, but no need to have the same finish throughout the entire house.

I agree with Laurence. Also, if one room is visible from another room (open floor plan for example), you should coordinate the finishes as well.

I like door hardware to match throughout the home but I think you can mix it up within a room and throughout the home when it comes to plumbing, cabinets and lighting.
There are articles on mixing metals within kitchens and baths in the ideabooks.

Colors in one room / space should be same or similar; i. e. Chrome / stainless okay and even shiny or brushed together is okay. But I would be reluctant to mix gold or black or rubbed bronze in the same space, Not a design rule, just a preference. Consistency makes it look like you have a plan.