Take the rifle and put it on a shelf ... 70+yrs ? No gunsmith is going to say "looks OK to shoot" and anyone that does, I would avoid.
Assuming you want to keep it all original ... which you should
The two biggest threats to guns is rust and politicians. I'd think that using it occasionally is the best way to keep both away. People should not think of such rifles as relics, they need to be seen used responsibly.
I'm not sure this rifle has so much value as something to be on display. The Army had millions of these rifles made and they were not concerned about keeping the rifles it had in original condition, parts were replaced with new as needed. Good chance this rifle has already had parts replaced. I saw no markings on the rifle that would indicate it is rare. Best guess this rifle is worth about $800, mostly because that is what a new one costs from Auto-Ordnance. The value it has to me is that Dad gave it to me.
Unless it was damaged, there is no reason to suspect a GI M1 Carbine is not safe to shoot. Clean it, shoot it.
I'm concerned about bolt wear. If the bolt has worn to the point of having the chamber out of spec there could be excessive pressures produced.
I believe I need to explain my concern in more detail. I took the rifle to the range last weekend and I noticed that some of the spent cases did not have primers, this is an indication of excessive pressure. I had a mix of ammunition brands and all the cases that lost primers were of the same brand, Magtech. It's possible that the Magtech ammunition was out of spec. It's possible the rifle is out of spec because of wear. It's possible the rifle was damaged by that ammunition. It's possible I did not clean it properly. I'd like to have someone that knows what they are doing verify the rifle is safe to shoot.
I'm also dealing with the suspect ammunition. I called the store where I purchased the ammunition and they were unaware of any issues or complaints with that ammunition. They offered to exchange the ammunition with another brand, they agreed the ammunition may not be safe. I've not yet taken advantage of their offer.
Gander Mountain in Cedar Rapids does have a gunsmith in their store, depending on their work load they might be able to help me out quickly. Scheel's in Coralville said they'd have to ship the rifle to their gunsmith in Des Moines but the rates given were lower than Gander Mountain if I recall correctly.