What happens if a party wins a landslide in the direct election and does very poorly in the proportional one? This could boost the number of mandates.

Do they build a new parliament?

Otherwise many thanks for describing the german vote system.

Looks pretty reasonable to me, it allows local out of party candidates to be elected, gives proportional representation to country-wide small parties and fair share for "big" parties.

Are there any cases where the election results were considered "unfair"?