Potted palms kept indoors/on patios are more likely to be harmed by infestations of mealy-bugs or scale, or by ants getting in and building nests about the roots, or by worms getting into the potting mix and playing havoc with the drainage in the pot. I would not suspect anything crawly of being harm to the palms themselves, more likely some sort of slayter or such.

But if you are concerned, and the pot is small enough to manage this, you could try drenching it by dropping it in a bigger container of water, and leaving 15 minutes until all bubbles stop rising. That may drown your creepy-crawlie or at least bring it to the surface. If it does bring anything to the surface you can perhaps pluck it off or spray with pyrethrin. The exercise will at least give the plant a good drink as well as giving your muscles a workout. Let the pot drain away though & don't let it sit in a saucer of water after.
Of course, if you can CATCH one of the creepies, your local nursery or council may be able to ID it.