Is there any logical reason behind a way with only 1 node:
http://www.openstreetmap.org/browse/way/3428611
Or this one with the same node twice, but no other nodes:
http://www.openstreetmap.org/browse/way/127498962
No, no logical reason for those. They are errors, so should be corrected or deleted.
They should be highlighted on tools like OSM Inspector or Keep right, so you can have a look for them and fix any in your area.
http://tools.geofabrik.de/osmi/
http://keepright.ipax.at/