15 years ago I was a member of a parish in New Jersey where the "Assistant Pastor" was a lay woman. (She wouldn't have that title now, I'm sure.) She was very well qualified, with an M.Div. and an S.T.L., and provided a lot of continuity to the parish. The parish had experienced rapid turnover of pastors (always a priest) but she had remained the assistant pastor for well-nigh a decade.
She never, ever, performed any liturgical function.
She spent her time visiting the sick (also as an extraordinary minister of communion -- but not during Mass), counseling the troubled, doing marriage prep, planning liturgies, and assisting with the youth group. I'm sure she had various office administrative duties as well, but I didn't have cause to see those.
It seemed pretty much licit and fruitful to me. I'm glad I experienced
This sounds like a very positive use of the laity. In a time of a clergy shortage, the “lay assistant pastor” stepped in as extra hands for the pastor. It does not sound like she usurped the priestly function or appearance in any way. She does not sound like a replacement for the priest, but rather an adjunct to the priest. Her position in no way undermined the office of priest.
Rich Leonardi addressed this issue as well with his post here. Pay special attention to the words of Cardinal Arinze:
If a diocese does not have enough priests, initiatives should be taken to seek them from elsewhere now, to encourage local vocations and to keep fresh in the people a genuine "hunger" for a priest (cf. John Paul II, "Ecclesia de Eucharistia," No. 32). Non-ordained members of the faithful who are assigned some roles in the absence of a priest have to make a special effort to keep up this "hunger." And they should resist the temptation of trying to get the people accustomed to them as substitutes for priests (cf. op. cit., No. 33). There is no place in the Catholic Church for the creation of a sort of parallel "lay clergy" (cf. "Redemptionis Sacramentum," Nos. 149-153,165).
Priests on their part should show themselves transparently happy in their vocation with a clear identity of their liturgical role. If they celebrate the sacred mysteries with faith and devotion and according to the approved books, they will unconsciously be preaching priestly vocations. On the other hand, young people will not desire to join a band of clerics who seem uncertain of their mission, who criticize and disobey their Church and who celebrate their own "liturgies" according to their personal choices and theories.
The situation Esperu describes fits the message of Cardinal Arinze’s address far better than the situation portrayed at Mary Queen of Heaven Parish. In the latter case, the priest is replaced and there is no sense that this is a sub-par arrangement. The “hunger” that Cardinal Arinze speaks of is suppressed.