Brian Weatherson of Cornell has an interesting little post here. I have to say, though, that it seems he's drawing distinctions without differences. Mainly because my intuitions don't line up with his at all. I see production as a species of causing (if non-intentional), and making as equivalent to production. Example: If the remote control's signal made the TV turn on, then the remote control's signal produced the TV's turning on. Either clause entails that the remote control's signal caused the TV to turn on. So, overall, I think that Weatherson has latched on to something parochial about the way he's using these concepts, not something about the concepts themselves.
This is not to say, of course, that he's using them wrongly or I'm using them rightly. Rather, it's that producing, making and causing are sufficiently vague notions that relying on intuitive understandings of particular propositions involving these concepts isn't going to get us anywhere. What we need is an analysis of the possible relations between events, which can be followed by "tagging" each of these relations in turn as one sees fit: "causing", "producing", "making", etc.
The caveat about intentionality matters as it's not at all clear (no matter what Davidson thought; and, I do know he's not the only one) that actions are just intentionally-described events, and, hence, are at some level events that can be caused. If actions aren't just special kinds of events, but are in some sense sui generis, and we treat "cause", "produce", "make" and so on as primarily applicable to events, then action-claims (e.g., "I caused the TV to turn on", "I produced the TV's turning on", "I made the TV turn on", etc.) must, at best, use these terms elliptically, non-standardly or in some derivative way.