"Kati is looking for doctors and finds secretaries."
Translation:Kati orvosokat keres és titkárnőket talál.
Neither of them are good here.
"Pedig could be used in an "and not" kind of situation, or in an "and he, on the other hand" situation:
Kati orvosokat keres, nem pedig titkárnőket - Kati is looking for doctors and not for secretaries.
Kati orvosokat keres, Péter pedig titkárnőket - Kati is looking for doctors, and Péter (on the other hand) is looking for secretaries.
And "meg" could replace "pedig" in the second sentence above:
Kati orvosokat keres, Péter meg titkárnőket.
Fair enough in general, but this particular course is too poorly structured (locations and preposition suffixes are drilled ad nauseum, while other skills are mentioned once and then hardly ever revisited in other contexts) and leaves out or glances over too many important parts of speech (possession?!?!? Just a single unit, yet it's a complex area) to achieve either aim.
I do agree with you. There's a lot going on in this course and often not in a very fruitful direction. But then again, Hungarian is really hard to teach to English speakers and the constraints for the courses are tight. Duo in general has a hard time with agglutinative languages, I think. There are only so many words a course may contain, and each variation is counted on its own.
This course is pretty okay altogether, but there are still many rough edges that have to be hewn out before it's enjoyable. (Also imperative! Where is it? It's so important.)