Dear Andrew,

The four things that you mentioned, minister, form, intent and matter: these are the requirements for transubstantiation to occur...  that is, the bread and wine are changed to the Body and Blood.  The Eucharist is "valid" as long as these four conditions are validly present.

I think it would be best to say that the "sacrifice is complete" though once the Liturgy of the Eucharist is properly celebrated, that is, the priest offers the gifts at the offertory, all of the preparatory prayers are said, the wine is mixed with a little water, the prayers of adoration, thanksgiving and petition are said, the priest receives etc...

Keep in mind though that actually the sacrifice is already complete..  that is, Jesus died on the cross.  Jesus himself is the priest.  To say that the sacrifice was not complete at this Sunday's Mass celebrated by father so-and-so would mean that only this particular celebration of the sacrifice was not complete.

In regards to the homily being omitted, the wrong readings read etc I wouldn't say that the sacrifice of the Mass is incomplete, rather that the Mass was simply celebrated illicitly, as would also be the case if the priest didn't finish the Liturgy of the Eucharist.

In order for the Mass to be invalid, and by that I mean no sacrament is present, there must be a defect in minister, form, matter or intent, for example the priest would need to skip the consecration or alter it into something irrelevant.  If the wrong Gospel were (purposely) read, that alone wouldn't invalidate the Eucharist, but it would be an illicit celebration.

If the priest for some reason did not receive the Eucharist, again it would be illicit, but the sacrament is still valid and present.

Hope this helps and if it doesn't let me know so I can clarify.

Mr. Slavek