One can put a small container near the work area to drop the threads in. Or do the lint roller thing to pick up the thread.
I've found that a wire pet hair brush works well to pick up threads off the carpet - I try to avoid getting long threads in the vacuum cleaner.
I do one last pressing from the back before the top gets sandwiched. Then if I find any iffy seams I can fix them right away. That's also when I try to get all those loose or longish threads trimmed or picked off.
My Mom also was a "it should look good on the back, too" person