I think a real dangers in the Charismatic movement are:
1. It pits the lay people against the Clergy, indirectly.
I have seen this in my own parish. The anointing of the sick is downplayed greatly. And the laying on of hands by Charismatics is hyped up. To the point where appointments are made to the healing ministry and sick people are coming daily to get hands laid on them by the ‘healing team’.
Blessed oil is used, which is put on the sick person and they are prayed over. Tongues often being spoken over them.
2. Church Authority seems to be downplayed (indirectly).
I think there is a real danger that Charismatics get caught up with speaking in tongues, the spirit “taking over”, healing powers, etc. That the Eucharist, Adoration, etc start to take a backseat even though they won’t admit to this. I believe it is easier for them to get sucked out of the Church or take part in non-Catholic services or functions because Charismatics themselves form ties with any and all who are supposedly “baptized in the Spirit” including those outside the visible boundaries of the Church. So that all those who are “baptized in the Spirit” or are “Charismatic” (Catholic or Not) are sort of the elite group and they are sort of seen as the “real” Christians.
I have heard some Charismatics say things like: “JPII is just JPII, it’s all about Jesus… in the end believing in what the Pope says or does or believing he is the head of the Church does not affect my salvation.”
Or:
“My faith in God has nothing to do with the Catholic Church, it’s about me and Jesus”
Disclaimer:
All of the above is just my own personal experience, i’m not infallible and could be dead wrong. Just calling it how I feel I have seen it to be.