After some more poking around, I've found that the following nations are present in the output from the World API's "nations" shard, but do not exist in the world:
ala_justice
amirala (appears in the output three times)
ariyacami
asdlfkjadfshlkjasdfkasdfah
bashikovia
bears_and_beets
bradguy (appears twice)
cels_rica
christellum
dalmactionmalix
dog_bubbarsbo
dovahianala
forica_pow
galizi
hiezenburg
hofus-pofus (appears twice)
leapland
linderville
line_archipelago
luxben
marxleninmao
morobiea
nethershland (appears three times)
north_lankton
otahahr
pepeion
place1
raptum
richtstenia
rooster_cogburn
san_dvil
terran_terras
the_free_state_of_orange
the_litro
the_next_future
the_republic_of_seventeen
type-48_light_assault_gun_carriage
vlodivinia
zum_daria
The following nations (at minimum) DO exist, but are not returned in the "nations" shard output:
freed_europe
not_a_puppet_iv