Update. I switched back to my original (red dot) bobbin case & thought all was well. Back stitches still didn't thrill me, but there was no (well, maybe ever so slight, occassional) eyelashing and no thread dots showing up front or back. So, I begin quilting. Now I'm getting skipped stitches and I mean real toe catchers sometimes when I go around a particular curve. I'm doing feathers and the skip is when I go around the fat curve on the feather to the left of the stem. Don't think it's a speed issue as I am going way slower than I'd like. So I rethreaded the machine & bobbin, putting a little drop of oil on the wick. Confirmed proper insertion of the needle. Manual says the problem could be cheap needles or thread. Definately not the case with either. I'm using needles and tension as per Tammi's post above. And I'm using the Janome bobbins. Still getting occassional toe catchers.
Thinking back some more, this is the first time I've used the machine since it had it's first service from the dealer. I wonder if he could have done something to it? I noticed after I picked it up that one of the spool holders was a little bent and scuffed. I wasn't having any problems before this and only had it serviced because I'd read you really should take it in once a year. Now is when I add that the Kenmore has never, ever, ever been to the shop since she came out of the box.
When I'm able to face the machine again I'll try a practice sandwich with cotton threads. I'm only using the Bottom Line because I loved it so in my bobbin for piecing and the color I have just melted into the backing it matched so well. So I bought another spool of Bottom Line to match the front of the quilt thinking that if I used the same brand & weight in needle and bobbin all would be well. Not. So. Much.
Again, thanks to all of you kind, understanding people for your input. Now I have to go iron my hubby's white business shirts. My joy is complete.