Butter can go rancid. I use a butter mill. It's terrific. You put a stick of butter inside it then turn a crank. On the opposite end is a slit where the butter gets pushed through, creating a wide ribbon of the stuff. It's small enough to easily store inside a refrigerator door, but won't fit in the dedicated butter drawer.
After about 9 months of using it, I started to notice a slight rancid smell. Apparently the butter remnants in the pusher had started to go bad. And this is something that was kept in the refrigerator all the time. I was using unsalted butter too.
As long as your room temperature seldom goes above 80 degrees, it's probably OK to keep some salted butter in a glass container on the kitchen counter for about 5-7 days. Search on the Internet for this as well... you'll find a number of useful websites rather easily. Note that rancid doesn't mean dangerous. It just doesn't taste pleasant, but isn't harmful unless it's allowed to be rancid for a really long time.
If I didn't have the butter mill, I'd probably get a butter bell
. They're pretty neat in design.