I've had my AR-15 for over three months now and have never noticed rust.  Today I took it to the range, and when I picked it up out of the case, I noticed rust.  It's enough to leave a tiny bit of brown on a tissue when I wipe it.  Of course it isn't on the aluminum parts, only the safety/fire switch, the sights, the trigger, the FA, the ejection port door, the takedown pins, magazine eject button, and even a little on the muzzle brake.  The screws on my scope mount are also rusting.  There is also rust on my .308.  Can this be a serious problem, and if so what can I do about it?  And why is it only rusting now when it had over three months to do so?

This is not unusual.  Most of my matte blued guns will leave a brownish stain on a cloth when wiped with oil.

Just keep CLP on everything, don't store the gun inside a case, and check in on it frequently.

Sounds like it's ruined.  Better send it to me for proper disposal.

So is it actual rust or is it something else?  Best way to remove/treat without ruining finish?  Just some CLP?

I noticed one tiny little spot on my barrel

The fact that you seem to have everywhere makes me wonder if you’ve got a storage problem.  For example (though I can’t imagine it being your problem), steel will rust pretty quickly when exposed to acid fumes.

More likely would be storing the firearms near, say, your bathroom, where the humidity can cause problems.

And, as Ken_Mays says, don’t store them in cases.  If you really want to keep them in something, look at the Bore Stores storage cases sold by Brownells.  These are breathable and won’t trap moisture like most gun cases.

Finger prints and hot humid weather.

Wipe it down with an oily rag after handling and get a dehumidifier.

If its a soft case, the nylon or padding on the interior may be retaining ambient moisture. I've found the same thing happening from the foam padding in hard cases like in the supposedly airtight Pelican cases.  You might want to try throwing a couple packets of dry silica crystals to absorb the moisture.