I think you should include other natural resources in your function. By convention "K" refers only to physical capital that is manmade--buildings, oilrigs, tools, trucks, etc.

In addition to natural resources, such as water and land and sunshine, I think one should also add in kinds of capital other than physical capital. In particular, both social capital (primarily education) and moral capital (values such as the work ethic or honesty) should be included.

Also, production includes wastes, and it is costly to recycle or dispose of these wastes; I think a production function should take account of these wastes and costs related to them.

I know it is wise to keep your number of variables down, but the availability of financial capital is also a binding constraint on production.

There is also the question of how to measure inputs: Do you measure them by dollar value or in some other way. One problem with using money as a measuring stick is that the value of money changes over time--so how do you measure capital that may have been built twenty years ago? Also, using only money means that one tends to neglect external costs and benefits--though one can put dollar values on these, it is a dubious process.