Well, Intel Pentium D and Pentium Duel Core are both old duel core processors, and if someone is trying to say it is new then you are being sold a load of crap (they are not bad, just not new). Core i3 is a modern duel core processor (newer ones have hyper-threading I believe making them a fake quad core) if you are looking for something with a decent balance of horse power and battery life I would go with one of those. AMD also makes duel core processors in the Athalon 2 x2, and Phenom 2 x2 (the x3 is a 3 core, and x4 is a quad core). AMD also has some APU products out that supposedly have a great bang for your buck, but I am not sure how they perform against other platforms.
Do a ton of research before buying a laptop. There are several great laptops, and several really crappy ones. Read reviews, find the problems and weather or not they would affect your use of the laptop, and then go to a store to use one before buying it online. For example, HP had some laptops out about 2 years ago which looked great on paper, but then when I saw it in the store there was this textured design on the touchpad for the mouse! I mean what moron in their right mind would sell a product that annoying to use? Sure it looked pretty, and had they made it a flat surface it would have been fine, but as it was it was a complete deal-breaker. Things like that tend to get overlooked in reviews, so definitely use the product you plan to purchase, even if you dont buy it from the store you try it at.
Dual core is a generic term. It applies to any CPU that is made by any company that has two cores in them. The Core i3-2310m is an example of a dual core CPU. Even some smartphones are powered by dual core CPUs.