I've really liked this song for decades. Thanks to your thread I've realised I haven't seen my copy of "Steam Ballads" for at least ten years. I probably confused it for a duplicate of "Steam Whistle Ballads" and deleted it...

"Moses of the Mail", is I think a sarcastic title. We can imagine Old Mr Poyser pootling along on his decrepit Lancashire and Yorkshire locomotive doing his nightly freight trip from Manchester to Warrington and back.
Thorpes Bridge Junction, just south of Newton Heath, is where the Oldham Loop diverges from the Calderdale Line. Mr Poyser took the Calderdale Line.
Presumably "Moses" was white-haired and bearded. His hair may have been "wildly waving", but he wasn't "speeding through the air" at Thorpe's Bridge Junction as he stopped straight after the junction for an "on" signal opposite the loco sheds at Newton Heath. His old locomotive will have needed regular oiling round as it chugged through the night and its sandboxes would need sand to spread onto the wet rails for extra grip.
Moston cutting is dreary.
If the fire was full of clinker, then the engine wouldn't have steamed very well. This is probably a more sensible version but doesn't sing so well. If both injectors didn't work then the boiler wouldn't have got any more water and the train would have been stopped. "Front tenders" is meaningless and McColl should have known better. Perhaps "Both front sanders" is the better option: maybe the sand got wet as the fireman was filling the boxes at Newton Heath. Perhaps the engine wouldn't steam as the fire had got low while the fireman was out of the cab.
Hopwood was a suburb of Heywood, which is now Oldham. Castleton East signal box is (or was) there, and controlled a diverging line which is now the East Lancashire Railway and which used to go to Bury.
By implication one of the slower moving bearings on the engine was "growling" and so needed a bit of lubrication. That's why "Moses" reached for the tallow pot (I'd always wondered why a steam loco had a teleport fitted.) He'd have had to stop again to lubricate the bearings. Isn't a broken collarbone quite nasty?
This Castleton is a suburb of Manchester, not the lovely Castleton of the Peak District. That had me confused too.
I don't know why they wanted to reload wagons at Hebden Bridge, perhaps it's because "reload" rhymes with "road". I imagine the train would stop if some of its wagons had derailed.