I'm in the middle of doing this cake, and my buttercream, which I've made so many times before, has tiny butter pieces in it, how do I get rid of them????

Sounds like your butter was too cold. I would probably just keep beating it until they softened and mixed in.

Ageed -- Just keep beating.

OK, thank you for your help, I will try!!!

Sometimes I will put a bowl of warm water under my mixer (as its mixing) to help melt the butter a little. Not too much or you'll end up with soup.

What type of icing were you baking?

Yep! Turn that mixer on and go watch an espisode of Seinfeld or something. (I used to turn on my mixer, then walk next door to the Dollar General store to visit with the girls over there, or walk to the Burger King on my parking lot and get lunch, have a smoke break and by the time I was back, I had perfect icing! )

If beating it for a few more minutes doesn't help, dip the mixing bowl bottom in warm water for a minute and stir until they start to melt again and then put it back on the mixer. It happens.

This happened to me a few times. the first was when i was making a wedding cake. When it happened again a few days later the only thing i had done different was use margarine that was not refrigerated and was very soft. Never used butter that had not been refrigerated again and never had the problem again. I've been making cakes for over 30 years.
Debp