Where should I take the temperature readings while mashing?

Mash temp can vary greatly and depends a lot on your mash tun geometry, the ambient temperature and your tun's insulation. It also depends on how you are delivering heat to the mash and how well you are circulating/stirring the mash to distribute the heat evenly.

If you are talking about a simple infusion type mash, the highest temp will always be in the geometric center of the grain bed (assuming you've first stirred it thoroughly). The mash will then cool most rapidly around the exterior where the heat can leak away the fastest. The most dramatic temp differences I've experienced in an infusion mash have been in square picnic coolers where the difference between the center and the corners (where there's a lot of surface area for the heat to leave) could be 5-8F lower than the center after just 30 minutes.

In contrast, if you have some sort of a direct heating element, then you want to measure your mash temps much closer to the heat source to avoid denaturing enzymes. And if you are direct heating AND recirculating, you'd best be served by TWO temp probes, one close to the heating source and one in the center of the mash.

Finally, one note on recirculating/stirring the mash. It can take a longer time than you think to even out the temps in a mash. The extreme case would be manually stirring a square picnic cooler--here a minimum of 5-7 minutes of thorough mixing seems absolutely necessary. The good news is that, once mixed, the mash simply cools off--so no new hot spots develop (which is really all you need be concerned about).

Bottom line is, you want to try to monitor the temp of you mash's hottest portion which (at equilibrium) will be the CENTER. However, if you have a heating element/direct fire you need to also play attention to the thermal effects of that localized source of heat, so a second temp probe is the best solution.

I have another answer. I've seen people doing it in many ways, and the only true rule I saw is:

consistency = good quality

Be sure to do it the same way every time, and adjust your temperatures if you miss desired results, and pretty soon your beer will turn out the way you want it to.

I usually stir the mash before checking the temperature. If you stir it, wait one minute for the thermometer to adjust, you should get the same temperature anywhere in the mash tun.