On Producteev you can move a task to another project from the task detail panel, right here:
You only need to take care of one little detail: all the people related to that task (assignees and followers) must be present in the destination project.
If the destination project is private and some people quoted in the task are not this one you have two options:
- You can delete those people from the task.
- You can add those people to the destination project.
That works well for the web app, but there is no such drop down menu in the Mac app (at least not that I can find).
I frankly find the Mac app quite annoying. Apart from that missing feature, it also lacks the ascending/descending switch in the iPhone app, and it always reverts to "sort by: last changed" when you relaunch the app. The worst bit is perhaps that there is no offline functionality in any of the Producteev apps. That is a shame as it is otherwise a very tidy and user friendly service.