When a paper is published with a particular list of co-authors, the assumption is that all co-authors participated in the work represented by the paper, that all have read and approved the submitted version of the paper, and therefore that all agree with the content of the paper. That last assumption, however, may have a substantial gray zone in which various authors have different opinions about how the work is presented.
A mild version of this would be if a co-author would have written the paper in a different way. This may well be the case for most papers, as we all have different styles of writing and preferences about how to construct an argument.
A more complicated version of co-authorial disagreement occurs when co-authors disagree about major aspects of the substance of the research that will be presented in a paper. For example:
Let's say that you provided some important data for a colleague's research project, and the colleague is now writing a paper using these results. The plan all along has been that you will be a co-author on the paper, but you find that you disagree with the colleague's interpretation of the data. It is not possible for you to reach an agreement on the interpretation, but it's also not possible for the colleague to use the data without somehow mentioning you or your lab. The colleague needs to finish and submit a manuscript using these data. Do you:
1. Let the colleague include your name as a co-author anyway but perhaps include some sort of indication that not all authors agree with all aspects of the paper.
2. Ask that your name be removed from the author list, and have your contribution indicated only in the acknowledgments section of the paper.
3. Refuse to let your colleague use the data.
4. Let your colleague use the data however s/he wants, but write your own paper with an alternative interpretation.
In many cases, I don't think options #3-4 are feasible, and these can be particularly problematic if students and/or postdocs are involved.
I think I would go for option #2, perhaps also asking that the authors include a statement that the interpretations are theirs alone. I have seen examples of this in the literature, and it can be done in a non-weird, professional way.
A long time ago, I was a co-author on a modified version of option #1 and it worked pretty well. In that situation, option #1 was acceptable to me because other authors agreed with me about our preferred interpretation, and the group as a whole worked together to find a way to represent all of our different points of view. In that paper, we presented the data "objectively" and then included two possible interpretations in the discussion. I don't think I would have gone for a version of #1 that was too far away from my preferred interpretation; in that case, option #2 would have been more reasonable.
Have any of you been in a situation in which you were an important-but not-primary-participant in a paper, and you disagreed with the interpretations of the lead authors? What did you do?