Not sure what the purpose of your question might be, however, some comments ...
The forecast QNH is representative in accordance with the BOM’s explanatory material quoted above.
That's fine. BOM is maintaining their defined reporting standard.
1013 hPa is exactly sea level pressure in the ISA.
Not quite but close enough for Government business
1 hPa = exactly 30’ in the ISA.
Not the case, other than at one specific altitude, which is of no great interest to pilot folk. Providing you are in the lower atmosphere, the error is not great. However, get up in the flight levels and the 30 ft/hPa is way out of line. Some discussion here
Bob Tait's Aviation Theory School - Altimetry Rates - Bob Tait's Aviation Theory School Forums
might be of use for those who are interested.
I presume that you are suggesting that the atmosphere on the day has a pressure distribution which is the same as postulated in the ISA ?
The temperature is exactly ISA.
I presume you mean both the standard SL OAT and standard lapse rate ?
Your altimeter is perfectly accurate and you are flying over the sea.
If you wish.
Your aircraft’s static source is at the same height above the sea as the altimeter.
Not generally the case, but OK.
Your altimeter is indicating 500’
OK
Question: What is your altimeter’s actual height above the sea below?
I suggest very close to 500 ft assuming you are nearby the departure aerodrome as the instrument check would have been done by comparing a known elevation for the test point to the instrument indication ie the BOM tolerance is irrelevant at this point. Which answer were you running with ?
Background to question 2.
Not too sure what Q1 and Q2 refers to, but, let's not worry too much about that.
assume that both altimeters in your aircraft were exactly 50’ ‘off’ in the same direction
Fast forward two hours and 150 nms, when the circumstances and assumptions as are set out for question 1 apply. But you now know that that the altimeters in the aircraft have a 50’ error.
Question: What is your altimeter’s actual height above the sea below?
I suggest, again, pretty close to 500ft but, assuming we remain in the same forecast QNH area, we might see up to the relevant difference for the BOM tolerance. I'll leave you to run the actual sums or look up an approximate figure from the linked reference. We would expect to see an error related to the 50 ft altimeter check error. I don't believe we can be certain what that error might be.
The question gives the answer for the QNH margin of error : +/-5hPa is +/-150ft.
But, as noted before, that figure is incorrect in this case where the OP is looking to split hairs.
However, is the static pressure source perfect ? I will assume so.
For the purposes of the question, one would include the plumbing in the statement that
Your altimeter is perfectly accurate
In real life, there will always be a small error due to propwash on the ground and relative wind in the air.
Providing you have zero sideslip, no. The purpose of the quite lengthy certification flight test work done to establish the AFM PEC data is to cover all this sort of stuff.
In practise, I rarely noticed more than 1-2 hPa of error when applying the right QNH on the ground
Not the point in question. Using A/QNH data, you may only assume the accuracy declared by the BOM.
I think this error will only ever increase with altitude,
Why is that ? You have no indication regarding the source of the error which you observed on the ground ?
because if 1hPa is 30ft close to the ground, it's more (much more) up in the air.
Close to sea level, the rate is around 27 ft/hPa. Indeed, it does increase with height as that is the nature of the equation for ISA pressure variation with height.
The effect won't be very noticeable at 500ft (1hPa = 30.5ft)
Only because I'm totally confused, whence comes 30.5 ?
That's ok for the purposes of this question
Not really, as the OP is playing with splitting of hairs, so the pressure rate variation becomes materially significant.
Hopefully, I will learn some material techo stuff with the OP's response ?