You shouldn't end up cleaning up after your trace. Better adjust the options so that the trace is clean.
It’s the Minimum Area setting in Tracing Options that will help you get rid of small pieces.
The larger the number, the cleaner the trace will be.
Use it with discretion all the same and click on Preview when you think it’s about right.
Now you tell me! :-)
I was in a hurry... I will practice doing the tracing options so that it turns out cleaner the next time around. I just couldn't get a good trace AND no little pieces yesterday. Obviously I need to play with the settings more. THank you!
I also find that when tracing high-res scans of B&W art, AI leaves an unnecessary layer of white underneath the black (making the file twice the size it needs to be). You can direct-select-click a black edge, invert the selection (option or alt-drag) to get the corresponding white path underneath, then Select>Same>Fill Color, and delete.