Quoted:
I have an older (Core 2 Duo 2.0Ghz, the generation before Santa Rosa, I think) Macbook, which I currently an extended screen onto a 17" LCD monitor through a VGA connector. I'm thinking of getting a 23" widescreen LCD to use with my new PS3, and wondering if:

a) I'd be able to do extended screen (i.e., run the MB's monitor and the 23" at the same time)

I don't see why not. The biggest limitation there is the max resolution that your chipset supports.

b) Whether I'd need to get a miniDVI-DVI adaptor to replace the VGA adapter I have at the moment.

Right now you are using the miniDVI to VGA? This is going to depend on the display inputs. I've got a pair of Acer 22" widescreens and they have both DVI and VGA inputs. Check the specs for the monitor you are interested in.