If I wanted to swap out processors in my laptop, what things would I need to look out for?

Intel and AMD mobile cpu's use different sockets on laptops, S1 for AMD Turion and Socket M for Core solo / duo. It wont be a straight swap.

Also the possibility exists as its a tablet pc is the cpu is not upgradable at all, as in order to keep a slim, low profile machine the cpu's are sometimes soldered straight to the board.

You need to find out what chips your motherboard supports (e.g. Intel core 2 quad, Pentium 4, AMD Turion, ect.) as well as what sockets it supports (e.g. socket 775, socket 462, ect.)

I'm not sure if you could swap your processor in a laptop, but do some research on google and fine out.

the two are not mutually interchangeable.

like in the stable platforms, the two companies use different sockets (the "docking station" of the CPU) because of that, you might end with a US plug vs Euroean power cord problem :(

find a CPU from the same socket family. when switching companies, you are most likely about changing the motherboard and THAT would be a real problem in a notebook, IMHO.

apart from that, you need gentle manipulation, definitely the heat conductive paste, and experience in replacing the CPU cooling fan and radiator.