Detergent may not be rinsing out completely.

Try using less detergent and use white vinegar in the rinse dispenser.

Wash pants wrong side out and see if that helps.

That's an interesting problem. This happens with EVERY piece of dark clothing or just with particular ones? And it always takes a week to show up? How large are these white spots? Are they uniform throughout the garment or just a few locations?

Do you add detergent with water in the machine? Most laundry detergents contain brighteners and other chemicals that can effect the garment if applied directly.

Have you tried a different brand of laundry detergent? Have you contacted the manufacturer of the detergent for any suggestions?

I think it's excess soap in your laundry. Suggest re-washing them, then add vinegar (white or cider) to the rinse.