I've heard different priests either say or omit the word "and" in the following context:  "In the same of the Father, [and] of the Son, and of the Holy Spirit."

The second "and" is always used, but the first is sometimes used, sometimes not.  Liturgically, in Latin, "et" seems to always be used twice.  However, when using in English, say when a priest is leading the Rosary or some other prayer, it seems to vary.  Is one way correct, or is either acceptable?

There's also "In the name of the Father and the Son and the Holy Spirit." ... where they skip the subsequent "of the".  Still valid, because the English language is base off of position rather than word ending.