For me, the trampoline. My theory was: that joke book somehow ended up on the roof of one of the wagons, and I need the trampoline to get up there to look around. I tried all sorts of stuff to get Ransome to land off-center and be flung at an angle. What I didn’t consider was that the tramploine was not needed yet.
The puddle also didn’t seem to make sense to me, although I had already read the spoiler by accident. Only when I saw the effect of pouring the waste into the puddle did that one click for me.
Also: the way I figured to catch the radioactive waste in the trophy was because it was the only vaguely container-shaped object in my inventories. I didn’t know the word “pewter” except in the context of “metal that’s used for little figurines”. I just looked it up, turns out to be mostly tin with some other elements, and sometimes a bit of lead. I’m guessing the lead variant was more prevalent back in the 80’s, but I still don’t see how something that’s at least 85% tin (and therefore at most 15% lead) would be such a good container for radioactive waste. Especially since it’s an open container.
No idea. Seems like we had a lot more time and energy back then though.
Some random answers to previous posts:
Hahah, reminds me of the great hint in Discworld: “Come again later. Or earlier.” 
Same here. Tried to enter the bank at the beginning and it was closed. I was waiting for an act to finish, and the time changing from the evening to the next day. I never received any hint that would indicate that the bank would be open by now. It seemed logical to try the bank again anyway at the point in the game when I needed it, but only in a “it doesn’t make sense, but let’s try anyway” kind of way.
That didn’t pose much of a problem, but I had to look up the values for nickel and dime since I’m not American, and therefore do not know all their quaint little words for arbitrary amounts of money.
Franklin can manipulate electricity. He zaps the phone, opening the line. Then he zaps the buttons to dial a number. At no point in time does he pick up the phone though; the phone remains firmly on the hook.
I didn’t find this all that illogical after seeing him manipulate the elevator panel to go wherever he wants. He doesn’t physically press any buttons there either.