Can I buy a development card in the special building phase that occurs between player turns?
Taken from the 5-6 players rules pdf: http://www.catan.com/files/downloads/settlers_5-6_rv_rules_100107.pdf
• Special Building Phase – Your opponents may build as outlined below. The Special Building Phase occurs just after the end of your turn (i.e., between player turns). All the other players may participate in the Special Building Phase. Each player then takes his turn clockwise around the table, and is allowed to build anything he can create with his resources. 3 Note that no player is allowed to play Development Cards during the Special Building Phase. Also note that players are not allowed to do any trading with other players—nor are they allowed to use Maritime Trade—during this phase. They may only use the resources they have in their hands. For this reason, players are advised to trade as much, and as advantageously, as possible with the current player during his trading phase. They will then have the resources they need to build during the Special Building Phase. The Special Building Phase is an opportunity for all the other players (who are not currently taking their turn) to build roads, settlements, and cities, and/or to buy Development Cards. This phase allows each player to influence the game, even though it is not his turn! ...
This is also supported by the catan faq:
Development Cards in General - If I have bought a Development Card during the special building phase right before my turn, may I play this card on my turn?