A lot has come from the bug recently where hats that were store bought (not usable in crafting) were then sold to unsuspecting buyers at "craftable hat" prices. The bug is now fixed but essentially didn't show that a hat wasn't usable in crafting while trading in-game. Don't be ashamed - it even fooled those of us who are supposed to know better (ahem, Jason). These hats are considered "dirty", which has become a blanket term for anything marking a hat. A "clean" hat is tradeable, usable in crafting and often also means there is no craft #. Remember that an item with a craft # higher than 100 can only be seen in a backpack viewer. A "dirty" hat is either untradeable (without giftwrap), or has gifted by text, or now is also not usable in crafting. Hats that have craft #'s are also considered dirty by many, but when trading generic items with normal values it is often not mentioned. It mostly has an effect on prices of higher-value items such as Team Captain or Cremator's Conscience.
There is a dirty discount associated with these hats. Typically a reclaimed metal off the craft hat price. Many of these hats now sell for around 2 reclaimed metals, which is about the right price in our minds as well. The hat looks the same but you just can't craft with it.
