Question: Colossians 2:18 is not clear to me, and the part about the visions puzzles me. Please explain.
Response: Here is how I have translated the verse (in part 2A of "Coming Tribulation"):
Let no one gain control over your life, desiring to [enslave you to himself] through a show of false humility and the adoration of angels, basing his approach on what he has [allegedly] seen while puffed up by his own fleshly thoughts, yet not embracing the Head [Christ].
The NASB translation, generally a fairly literal one, uses "visions" to expand the "what he has seen" part (they do put it in italics to indicate that they have added this to the text for interpretive purposes, a practice begun by the KJV), but there is no direct mention of "visions" in the Greek text. This verse is a warning against false teachers and false teaching and is specifically addressing the practice of claiming to have had special revelation from God of the sort that gives such a person an exceptional authority surpassing that of his hearers. "I had a dream!", cry the false prophets of Jeremiah 23:25, but God says of them "How long will this continue in the hearts of these lying prophets, who prophesy the delusions of their own minds?" (v.26, NIV). The "things seen" here may be described as "visions", but they are clearly not from God (even though that is what these people claim). That is why I have glossed the translation above "allegedly", because the text here allows for the possibility that 1) such individuals have simply made these things up; or 2) they have deluded themselves into thinking they have seen a vision (through self-suggestion, or drugs, or fasting, or mental problems, or some combination of these things), or even 3) they have received "visions" all right, but from a satanic source and not from God.
The translation above "let no one gain control over your life" (from katabrabeuo - to "lord it over" someone) indicates that we Christians must be very cautious about surrendering our allegiance and will to those who make the claim of having a special "in" with God, receiving private communication from Him whether by dreams, or visions, or appearances, or any other non-verifiable non-biblical means. This is very easy thing to claim, but I would be very surprised to learn that it has ever been true (since the apostles, that is), or will be again until the end times begin. All indications from scripture are that we are in a period when the Spirit is working through the Word of God, not extra-biblical revelation.
The "worship of angels" was a very large component of many heresies in the early Church (note the emphasis on warning against this in the book of Hebrews, and the attacks on Gnosticism in Ephesians as well as here), and is likely to be so again in the future, especially during the Tribulation when the unbelieving world will see signs and miracles performed by the power of the devil. The angels worshiped here are proffered as being elect, but are actually fallen, so that there is really not much difference from worshiping angels generally and outright devil worship (only a matter of superficial form). The last part of the verse "not embracing ... Christ" makes it clear that people who take this approach are not, in fact, even Christians. Clearly, to worship angels instead of Jesus, and then to exploit people with false teachings based on this approach, gaining influence over these poor victims through lies, is not of Christ, but of the evil one.
You might have a look at the following links as well:
Reviling Angelic Beings
Gnosticism and Angels
Yours in the One through whom we have already been victorious over all such opposition, our Lord and Savior Jesus Christ.