Unless you are doing massive compendiums, I recommend just to babysit things by the first author. Think collaborative writing programs or tracking are more of a pain than they are worth.
Have anyone sending proposed edits do so in MS Word with track changes. To you, first author, directly, not to the group. Use separate mailings, not group ones, to avoid reply all spam. Sometimes, they will need to send numbered suggestions or the like, but just process those than.
Use numbered version control for the files for each generation of the paper. Compile the suggested edits, drafts, reviews etc. in an electronic folder (subfolders if needed.) I really doubt you need to go back to the suggested edits much, especially if you process things in turn, but at least they are there. If people don't rename the Word file (often they won't) than you do so when you save (usually with some name and date associated with the review/collaborator). If they have emails with edits or the like save those into the folder also or into Word files (again renaming to be clear).
Resist the impulse to let a paper become a committee report. Have a clear leader (first author) and make decisions. It is fine that reviewers or collaborators got to make suggested edits, but you should view that as enough of a gift and then make the hard decisions. Sometimes you can even blame it on conflicting edits (truthfully or not).
Of course, you should carefully consider input and use it. But DON'T be a reed in the wind. Be a leader. Papers need that. That is a gift also. Truly.
[All of this applies to joint work product in the corporate world as well. Give people a chance to "have input" so they feel a part of the process. But be an owner/leader of the end product and not a compiler.]