my 03 have this particular problem and a lot of other 03+ as well.
my problem started just last year around october. start up the car cold to warm up - it will stay up around 2300 rpm or so and all of a sudden, the rpm would be jumping up n down.
it's similar to when you are revving your engine - like that. no, it's not normal.
does it hurt your car in any way, shape or form. i dont know, probably not.
did lots of research and asked around a lot, most people say it's to do with the IAC valve.
if you wish, you can try cleaning your MAF sensor to see if it helps. some people tried cleaning the coolant sensor.
for me, i chose to just leave it and live with it. i was gonna take it in to get it fixed but my warranty just ran out so i'm out of luck.
goodluck.