Fat can, and will go rancid over time. Oxygen, heat, light, and time all affect the time it takes fat to go rancid. I would never leave fat sitting on a pan and then reuse it, even next-day it will likely have started to go rancid.

I strain my fat, into an air-tight ceramic jar and then keep that jar, in my pantry (where it is dark). My jar looks something like this: http://www.amazon.com/RSVP-Stoneware-Grease-Keeper-Black/dp/B0017U5DZY/ref=sr_1_4

I do the same, pretty much is a seasoned fat, right. Nothing has ever happened to me. Just my own experience. You are not alone Jason.

I don't think there's a solid guideline on this; it's all about how far you're willing to go. Strictly speaking in terms of oxidation, it's safest to always use fresh oil, but that can be impractical. Oxidation happens gradually, and as long as you're not overheating the oil, you can arguably choose your own threshold for when to throw it out. Just pick an expiration point (number of uses or time) and stick to it.

Food safety isn't a binary switch, after all. There isn't a magical threshold for when oil goes rancid; when meat goes bad; or even when oil is overheated. The transition is gradual, and you just need to decide upon your own guidelines for the margin of danger you're willing to accept.

All fats will eventually oxidize when exposed to microbes, heat, light, oxygen, and so on, but the more stable the fat, the safer it will be when left out or re-used. You can try to extend the lifetime of the fat by reducing exposure to the aforementioned factors.