So your position is that reality is entirely deterministic, there is no "probability" at all in the territory?

I feel that is most likely, yes.

Is the forecast falsifiable, then? Can it be wrong? How would you know?

Same way you know if other probabilistic prediction systems are "wrong": keep track of accurate and inaccurate predictions, weighted by confidence levels, and develop model of the system's reliability. Unreliable systems are probably "wrong" in some way. Individual predictions that express extreme confidence in an outcome that is not observed are "wrong". But I cannot recall having reason to accuse any meteorologists of either error. (Full disclosure: I don't care enough to make detailed records.)

I would also point out that the audience adds another level down the predictive rabbit hole. Weather forecasts usually predict for a large area. I've observed that weather can be significantly different between Hershey and Harrisburg in Pennsylvania. The two are less than a half-hour apart, and usually have identical forecast conditions. This further confounds the issue by adding the question of who is included in that 30% chance of rain. You could interpret it to mean a high degree of confidence that 30% of the forecast area will see rain. I have not seen an interview with a meteorologist that addressed that particular wrinkle.

So the probability exists purely in the map, but not in the territory? I am not sure quantum mechanics would agree.

Can't speak on quantum mechanics with much authority, but my suspicion is that there's something going on that we haven't yet learned to predict (or maybe don't have direct access to) on a quantum level. I seem to remember that quantum physics predicts more than [3 space + 1 time] dimensions. Since I don't appear to have access to these "extra" dimensions, it seems intuitive that I would be as ineffective at predicting events within them as Flatlanders would be at predicting a game of pool as seen from a single slice perpendicular to the table. They might be able to state a likelihood that (for example) the red circle would appear between times T1 and T2 and between points P1 and P2, but without a view of the plane parallel to the table and intersecting with the balls they would really only be making an educated guess. The uncertainty exists in my mind (as limited by my view), not in the game. I suspect something similar is likely true of Physics, though I'm aware that there are plenty of other theories competing with that one. The fact of multiple competing theories is, in itself, evidence that we are missing some important piece of information.

I expect time will tell.

The status quo is certainly wrong when it comes to the presentation of weather related data. The report is badly oversimplified due to several effects including the (over)estimated gap in understanding of statistics between meteorologists and the general public.

A 30% chance of precipitation is not, however, "wrong" if it does in fact rain. It merely expresses a fairly high degree of uncertainty in the claim "it will/won't rain today". The claim that such a report means the meteorologist was wrong (or somehow lying) is the subject of my complaint, not the format of the report itself (which I agree is abysmally deficient).

Perhaps I could have better phrased the complaint; I wasn't attempting to dive into the philosophical. The point was that the meteorologist is not "wrong" if it rains on a 30% chance or if the high temperature is off by a couple of degrees. Meteorologists deal with a lot of uncertainty (that they don't always communicate to us effectively). People need to understand that a 30% chance of rain only means that it likely won't rain (roughly 2:1 against). Still wouldn't hurt to take an umbrella.

As for the philosophical, I'd have to claim that a Probability is a quantitative expression of predictive uncertainty that exists within an informational system such as the human brain or, yes, weather prediction models. Come to think of it, that might actually be helpful for people to understand the weather report. I just don't trust my coworkers to be able to parse most of those words.

Certainly it is easier to say it was wrong. Meteorologists actually do see the error bars &c., then they dumb it down so most people can grasp what they're saying. I understand there is ongoing discussion as to what kind of balance is appropriate between being precise and being understandable. Unfortunately, status quo bias seems to be dictating the outcome of that discussion, and much of the information in meteorological models is never provided to the general public as a result.

What precisely does "There is a 70% chance of rain tomorrow" mean?

It means that the proportion of meteorological models that predict rain to those that don't is 7:3. Take an umbrella. ;)