I live in Majorca with my family, and we have no problem cleaning our teeth, washing dishes etc in tap water, but we do not drink it. I'm pretty sure that it's not a hygiene thing - it's just that it tastes different, and I regret to say that the council workers are not very good at flushing through the system after they have been doing pipe repairs.
It is not unusual to run a sink of water to wash in, and have a sinkful of light brown water, after there have been local roadworks (it's maybe happened 10 times in 2 years)
The problem with Slush machines, the bigger Coffee machines, Ice Making machines etc - they are oftened plumbed into the mains water, and if the water is iffy then so is the drink, although I repeat that this is rare. At our bar we had a filter put on our mains, and it still tasted stale, so we had a second one put on (so it's doubled filtered) and we've not had any problem since. We also get our ice delivered by a company who guarantee that's filtered.
Judging from the number of Spanish people who stack their trolleys up with water at the supermarket, I think many locals share the same concern, so if you are on holiday, I would suggest that you buy a couple of bombs of water, and play safe.
Hope that helps a little.
Cheers
Adam