No, it's not mistaken—in fact, it's good English.
It's relatively complex grammar so you don't need to confess anything. Although complex, it's quite common for people to use this structure. It has essentially three grammatical parts to it and two different aspects, which I'd describe like this.
would (modal auxiliary verb)
have been (perfect infinitive)
doing (continuous)
The whole thing I would probably call a 'modal perfect-continuous'. I'm not sure what other teachers here would call such a construction.