Step 20: Use the Cheesecloth and Strainer to Catch the Seeds, Skins, and Parts You Do Not Want to Drink.
You can strain the wine a couple of times and get it pretty clear. Only one time around yields cloudy wine. It still tastes good though. More sediment reveals itself later by settling in the bottle. My guess is that the sediment is either yeast or sugar or some of both. Shaking the bottle up will alter the taste of the wine.