I made a cake last Saturday and have enough buttercream left over to complete a small cake for tomorrow. The buttercream has been refrigerated since last weekend. Do you think it will still be good to use?
Depends on which one you made.
I've only made the Wilton's course one (which is shortening-based), and my instructor said you can keep it on the counter (covered) for 2 weeks - and I have. Think about it ... when you buy shortening, it's on the store shelf, isn't it? You're not adding raw eggs to it, so it's good for awhile. Just stir it up before using it. But I do refridgerate it in hot weather.
What kind of BC did you use?
You are absolutely fine to use the BC from last week. I have had BC in the fridge for at least 3 weeks and it was good to go! Just let it sit out for a bit to warm up and take a taste. I am sure you will find it ok to use.