I propose an idea. Mainly because I am constantly shoving things in a crucible and then going “Wait, what’s in here?” and then I have to remove the hopper, get the shovel, dig it all out, and then reinsert into the crucible. It would make sense to me that if you use it on the top that’s open it would be able to tell you everything in the crucible.
Thank you for coming to my Ted Talk.
The Crucible intentionally only shows the topmost “lightest” Material, or the “something solid is at the top” Layer, I don’t think a Magnifying Glass Lookup would help you there. 
Maybe throw things into a Chest first and once you decided on what ratio you wanna throw in, take everything out the Chest and dump it in?
It usually happens when something in life happens and then I come back and I’m like “Wait, what did I put in? What am I making?”
Use the chat to write it down, even in Singeplayer, or invent time-travel so that you can go back in Time and ask your past self
Or sometimes you simply mess things up and wish to know what the crucible contains exactly. Like when you think you throwing in a pure metal, but actually it’s an oxide or whatever, and you mess up the ratio. Or when you do it intentionally, because NEI shows it converts to, let’s say, ½ of metal, but in fact it smelts to ½ plus 1/72 or else.
Speaking of crucibles, how can I extract liquid metal from a bath? Several times I manually stopped the burning box with the lever with no understanding why it pours my copper in the bath. A few minutes later I realized that it triggers the faucet. But why faucet doesn’t get activated when the thermometer passes signal through this noteblock to a piston beneath it. Anyway, is it possible to get my copper back? It can’t be cast into molds, and I guess I can’t pour it in a drum, lol.
Redstone is weird with Block Updates.
And you can just use a Measuring Pot to grab the molten Copper back out of the Pot?
I had weird experiences with the location of the lever in regards to what it affects, I’d play with where the lever is located.
