Hay is a very difficult thing to purchase and know exactly what you are getting. The risk of feeding suspect hay to a horse is not worth trying to save a few dollars on the hay. Here are a few things to look for when trying to determine if your hay is bad:

Visible signs of mold -- there should be absolutely NO mold.
Musty smell -- it should be sweet-smelling.
Flakes sticking together - almost matted -- flakes should fall apart.
Dusty appearance or mold spores falling out of the hay when you separate flakes - there shouldn't be any mold and minimal dust in the bales.

Your hay has two signs that tell you it might be bad -- flakes sticking together and a dusty appearance. Also check the stems of the hay on the ends of the bales very closely. The stems or stalks of the hay "wick" the moisture out of the air and up into the center of the bale. If the bales had a high moisture content to start with or got wet, you have a much higher chance of ruining the hay.

ANY mold or mildew on horse hay is not acceptable. A lot of times the hay will look good on the outside but if you break it apart it will look dusty and have a musty smell -- this is bad hay. There is always a chance that the hay came from a very dusty field, but this is not usually the case.

Different types of grass are more prone to spoilage than others and wet climates make it harder to keep hay too. Salting hay will help absorb the moisture of wet hay, but if your hay is already showing signs like this it's too late.
If you suspect you hay has any mold or mildew on it after thoroughly checking it, do not feed it.