I was just looking at stuff under the hood tonight and noticed little bits of dirt in the coolant overflow reservoir. Is it typical to see a bit of dirt/crap in there?

 

I have never owned a car (even new) that didn't develop the "crap" in the coolant reservoir after a while. Most of it is in the form of grease + microscopic rubber particles that form "flakes", due to the normal corrosion of the rubber hosing, dislodged and collected by the coolant fluid and deposited in the overflow reservoir (the highest point in the circuit, because these flakes float). If you open the radiator cap, you'll probably find some in there, too. Usually replacing the fluid gets rid of most of it, but there is always some left.
I would say it's not uncommon, just like the metallic powder in the oil pan. However, if it bothers or worries you, have it checked.
I'll have a look at mine later, when I get home.

 

Ya...its not dirt, but corrosion and just sludge in general that develops as your car operates.

+1 for flushing cooling systems as required.

 

Look for that radiator cap too