“ERROR” displayed on head items

As nimcap answered, unusual hats are just hats with special particle effects. They have no stat benefits, only visual effects.

The only way to obtain them is to trade for them or to find one in a Mann Co Supply Crate. Crates have a low chance to contain an unusual hat.

According to data gathered by users on the forums, it seems that series 1 crates have about 2.45% chance of containing an unusual item, and series 2 crates have about a 1.5% chance. You can tell which series of crate you have by reading the tooltip.

To open the crate you need to buy a Mann Co. Supply Crate Key, which costs $2.49 in the store. If you'd rather not spend money you can trade the crate to someone. Items that come out of crates are craftable and tradeable.

You can find more details about the drop rate on the TF2 wiki page about crates. Keep in mind that this data is gathered by players and might not be totally accurate, but it's probably in the ballpark.

The main difference between normal and Vintage items is that Vintage items are all the items people obtained before the Mann-conomy update. They can no longer be acquired in any way except trade. This makes them very rare. You can recognise them by their blue name only, since people could also just rename their items Vintage. Also, as pointed out in the comments, the "Vintage Tyrolean" and the "Vintage Merryweather" are renamed to "Vintage Vintage Tyrolean" and "Vintage Vintage Merryweather" respectively.

See the Mann-conomy FAQ:

Q: Why have all my items switched to "Vintage" items?

A: Some items that used to be rare will become more common when they are available for purchase. We wanted to give players this option, but still recognize people who obtained those items “the old-fashioned way” in the past. So we decided to perform a one-time conversion of all the old items into "Vintage" versions, which will never be attainable in the future. This way, those older rare items remain rare (in fact, they're even rarer, because they're limited editions now).

Basically, Valve decided that making items available for money devalued the items, since it is less impressive to buy an item then it is to craft/find it. Therefore they converted every existing item in people's inventories to Vintage items.

Since you can no longer create them (only the items converted at the update become them) Vintage items are very rare, which gives them a higher value in trade. Otherwise they are identical.

Additionally, a couple items are excluded, such as badges, promotional items (eg. Bill's Hat) and holiday items (eg. Ghastly Gibus).

Funnily enough, the Vintage item's rarity will increase over time, as people use them up in crafting.

See also: The Quality article on the Team Fortress wiki.