Flowering Weeds in My Yard (Erodium moschatum)

I thought this was a pretty sight when I woke up this morning, despite the work ahead. We have just gotten back from a three day weekend late yesterday. We mowed early last week, but it definitely needs it again. Dandelions, clover, and these unidentified tiny pink flowers have been growing the whole time.

I hand pull the clover and other creeping weeds and pop the dandelions out by the root, but it is a thankless task. We have a field across the street so it is practically impossible to control them in my yard without chemicals. I'd rather have the weeds.
Update: The small purple flowers are Erodium moschatum, also called filaree. My photographer husband took a better picture to show the detail. Much better than mine. :)