"La mujer busca las pistas."
when 'pista' means course it is often modified as a ski trail, autopista, racecourse, running track, etc. I suppose Duo figures she is not likely to be looking for more than one of those, so it goes with the other meaning: clue, scent, trail (as of a criminal), animal track, etc. Even if your version is correct, Duo may not have it in the database as such -- a not uncommon occurrence. ;)
why the present continuous form "is looking for" this time is marked as wrong, whereas in previous lessons it's always accepted? Is there a big difference in meaning?
exactly the same difference as between "looks for" and "is looking for"(that would be "está buscando")