What do I do to correct this problem?
De-nib, then either apply a little fresh finish (tips on that below) or polish up the varnish that's already on the piece.
If you don't mind that the surface is more of a satin or semi-gloss the simplest option is to just buff up the surface a bit after you de-nib.
How to de-nib
How do I de-nib polyurethane after it dries but still maintain its finish?
Note especially tip on using brown paper for this!
Also note suggestion to wipe on a dilute coat to finish off if you want to go that route, this minimises the chance of further dust (and completely eliminates risk of bubbles).
Also see Leveling a finish/finishing the finish
What went wrong on this last coat?
Can't be sure from the photo, could be either bubbles or dust nibs.
Most of us really have no control over dust in the air ultimately, even if you build a finishing enclosure/tent in your workspace there will always be some*.
Working in a normal room as most of us do you can dust the room carefully, vacuum and then leave for some hours for airborne dust to settle but you'll disturb a bit of it walking into the room, and additionally you can carry some dust in on your body and clothing. This is why in addition to clean rooms professional finishers may also wear a special garment that covers them completely (often including the head) and not their normal clothing which can be loaded with dust.
*Although a tent does go a long way towards reducing the risk nearly to nothing. But then wiping your varnish on practically eliminates the problem anyway, without having the hassle or taking up any valuable floor space.