Oil based paints are great for adding grime, but take a long time to set and can be wiped off. It's great for putting in details where it will hang on. My theory is that if it wipes off then it would have wiped off it it was "real." Along the same lines, pastels and chalks to add dirt and dust. Colors you might try are dark and light browns, black for general dirt and grime, you can also use green for greasy looking grime. The nice thing is that you have time to work it up and then wipe it all off. After you do this a few times it will accumulate natural layers and the places you have a hard time cleaning are probably the places that would normally be dirty anyway, so it will look more natural. You can use acrylics too, but they set faster and aren't typically as "organic" looking as the oils.
You can also use the method of brushing on something like olive oil then baking the part to oxidize it. This will be pretty permanent unless you sand it off. This is basically the same process as seasoning a cast iron pan.
You can use things like aluminum black as well, this will also be pretty permanent and durable.