Some of these thoughts originated in another forum, discussing songs that are not completely doctrinally correct. The songs mentioned here are mentioned because they were mentioned there. They may or may not be familiar to you. The songs are for examples and their use doesn't necessarily mean I endorse all their sentiment.
Some people seem not to care whether a song is doctrinally correct if they like it (tune, beat, tempo, etc.). Others seem so critical that they wouldn’t like the words of anything they didn’t write/right. Perhaps somewhere in the middle of this is the place to be.
I can think of four options a person might have for handling this: sing the song without comment; sing the song but with a comment about the problem; sing the song with altered wording; or don’t sing the song. There may be other options, but I can’t think of any right now. My personal opinion is against altering the wording of someone else’s hymn/poem. Either use it or find another hymn. It just seems honest not to tamper with someone else's song.
Here are some questions that might be helpful to ask when considering what to do with songs that could be "suspect".
1. What is the hymn writer trying to communicate?
Perhaps we may be overly critical of some point in a song when we don’t really understand what the songwriter is trying to say. "Lord, build me a cabin in the corner of Gloryland" – seems the writer is trying to express that he doesn’t deserve a mansion – "I feel I'm not worthy, to receive all of this" – and that a cabin up there is better than a mansion down here ("Don't care for fine mansions on earth’s sinking sand"). Not bad thoughts to express, IMO. I suppose the main problem is that it falls short of recognizing that Jesus has nevertheless promised us a mansion.
2. Is the overall message solid with a few questionable words, or is the overall theme of the hymn suspect?
"O What a Savior"; "they searched thru heaven and found a Savior" – the hymn writer used a literary device that doesn’t come off well in this song, IMO (though in Revelation 5, John seems to see something in a vision that uses a similar device). The writer is hopelessly straying in sin and a Savior is sought out to save him. Overall the hymn writer seems intent on glorifying the Savior, giving His death credit for saving even the vilest of sinners. He probably didn't intend to imply that God wasn't sure what He was doing and had to look around to see if He could find a Saviour. Yet it does give that impression to many people.
3. Does the rest of your church see a problem with these words? If not, could it just be you?
"There is a fountain filled with blood" -- Perhaps one might not like the particular poetic picture drawn by Cowper, but the point that the blood of Christ cleanses us from all sin comes through clearly. Not only my church, but many churches over several hundred years seem to have approved of the text. That doesn’t make it right, but should give reason for me to consider it carefully if I think something is wrong with it.
4. Is it a factual error, a doctrinal error or perhaps only a minor interpretational thing?
I suppose all errors are ultimately doctrinal errors, but a song that presents Jesus as not born of a virgin would be a different type of error than one that puts the wise men at the manger rather than a house, as Matthew says. Further, this factual error about the house is different from the interpretational error where some people interpret certain Old Testament verses as prophecy of this event and believe there were three wise men and that they were kings.
5. Is it wrong because it doesn’t tell the whole story, or does it tell the wrong story?
"Jesus is coming soon"; "all of the dead shall rise" – all of the dead certainly are going to rise. Perhaps the writer thinks all indiscriminately will rise at Jesus’ 2nd coming, or perhaps he believes the resurrection of the just and unjust will be separate and didn’t explain it in detail. Some think the resurrection of all will be at the same time, while others believe it will be separated by 1000 years or so. It seems that whatever one's millennial persuasion, most believe that "all of the dead shall rise."
6. What would you do if a preacher or teacher taught what is being sung? If he were a visiting preacher, would you invite him back? If he is the pastor, would it be ignored? would he be reprimanded? run off? Another way to put this is to ask if we are harder on our songs than we would be on our teachers? The songs are easy victims – can’t talk back, don’t get their feelings hurt and we don’t have to challenge them face to face. Someone criticized the song "My Sins Are Gone" because "...The chorus has a line that says, 'In the sea of God's forgetfulness that's good enough for me' but, one cannot find the phrase sea of forgetfulness in the Bible." How many times do we preachers preach using some phrase or word that is not found in the Bible?
7. Is there another song that expresses the same truth without the objectionable feature?
"Just a little talk with Jesus" was criticized because it mentions a little "prayer wheel turning" -- which is something Tibetan Buddhist monks do/use. Cleavant Derricks (1910-1977) was a black Baptist preacher/songwriter. The idea of a prayer wheel seems a little strange to me, but I find it unlikely that he had a Tibetan Buddhist prayer wheel in mind. More likely it was something like an attempt to describe a feeling that incited him to prayer. It is very unfortunate that those familiar with a Tibetan prayer wheel might think of that rather than what Derricks meant. Perhaps there is another song that similarly exhorts one to prayer, without such an objectionable phrase. This question should probably ultimately follow up all of the other questions. If we can express the same truth without the objectionable features, shouldn’t we do it? But also we should extend grace towards those who don’t come to exactly the same conclusions as we do.
Finally, remember that the only inspired songs are found in the book of Psalms! If we cannot bear to sing any perceived error, however minor, perhaps we should adopt the same mentality as some of the Reformed brethren – sing the Psalms only and exclude all hymns of human composure. Rather than that, I think I would apply some or all of the questions above and then follow one of three options – sing the song without comment; sing the song but with a comment about the perceived problem; or not sing the song.