...With Improved Special Effects
 

We had an argument today when someone played this card onto an item in the middle of combat. One side argued that items cannot be played/equipped in combat, the other side claimed that since it has no cost it is not an item...

I couldn't find an explicit definition of what makes a card an item or not. There are some treasure cards that are obviously not items (sidekicks form Super as an example), but this one resulted in disagreement.

Re: ...With Improved Special Effects
 

Cards with a gold value, including "no value" are items.

All other cards are not items.

Re: ...With Improved Special Effects
 

Then what kind of card is it? If it is not an item, then it isn't in the list of card types listed in here...

Which still begs the question of when it can be played....

Re: ...With Improved Special Effects
 

Non-Item Treasure cards do exist, so this particular situation isn't completely uncovered. However, this particular non-Item Treasure modifies an Item, and the rules state (with some emphasis):

Once you expose a monster card, you must resolve the fight with your equipment as it stands, plus any one-shot items you choose to play.

Since enhancing an Item would not be leaving it "as it stands," you can't play a card like With Improved Special Effects during combat.