Great info in this thread so far. The chart showing the relationship between phosphates, nitrates and the types of algae growth is very telling!
I too fought dinos in my system years ago when my nitrates and phosphates were at zero. Thinking at the time was nitrate and phosphate were too high (even though they were reading zero). Ran GFO and a fuge that grew chaeto like crazy and the dinos and hair algae just kept going despite ZERO feedings. Finally gave up and restarted my system 3 years ago.
To my horror, dinos started coming back a year into the new system. Nitrates and phosphates were at zero. My solution was to add more fish and feed more. My nitrates and phosphates are usually at or very near zero without GFO or a fuge. I can't get phosphates over .1 and nitrates over .25 despite feeding... a lot. Must be something in my rock, sand or skimmer that is consuming all the nutrients.
If I don't feed my tank 4 cubes of frozen food each and every day (when I am out of town and my family forgets to feed a few days in a week , for example) I notice what looks like stringy dinos start to establish in spots.
I also noticed the color of my corals improve since adding the fish and upping feeding. When nitrates and phosphates were 0, 0, the corals were much more pale.
As the chart says, you need to keep nitrate and phosphate in balance in relationship to each other.