Am in the process of installing 17.3 cinnamon 64-bit. I've downloaded the file, checked the sha256 and signature and copied the file to a flash drive. Is there any way to confirm that the copy is identical to the original or does the copy from the GUI check ?

Perhaps this will answer your question:
https://linuxmint.com/verify.php

I've already done that after downloading the file to my PC. Everything was OK. I've copied the iso file to a usb flash and want to check that the copy on the drive is still ok. The only thing I found was doing an MDF check from the GUI on each of the files the MDFs matched but I'm not too happy about only trusting that.

What, precisely, are you trying to guard against? You could try, though I have no idea whether it would work, running MD5 against the partition on the USB device or dd it back to a file on your hard drive and look for differences, perhaps?

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How did you 'copy' the iso to the flash drive? Simply copying in won't make it bootable. What software did you use to put the iso on the flash drive?

yes, you need to tell us how did you copy (and exactly what).
Usually we check if the download was successful, but usually we rely on the copy tool when we copy it onto the pendrive. (But obviously it depends on what did you really do).

I guess you could mount the iso image and compare it to the usb by a few ways..

Some few distro's offer a first boot check I think. You'd think it would be more common.

OK, I want to use the same iso for two PCs which is why I want to keep a copy of it. And then create another boot usb. Not 100% that I can use the same boot for both my laptop Lenovo and my Dell desktop. It seems like I should be able to do so but I don't want to have to download another iso - at least not until I've installed my new router and usb wifi adapter, the current ancient one took 2 hours to do the download. Right now I'm concentrating on installing 18.3 on the laptop - both it and the desktop currently have 17.3 installed.

I may be miss-understanding here.

If you downloaded an ISO then used dd or any other method to create bootable USB disk to install that OS, then yes, you can use that same USB on as many machines as you like (as long as the machine supports booting from USB).

Thanks all my problems solved. The boot usb is already created. Now to finish my backup to an external disk.

Not solved yet. The install stops. I see that the network communication to the pc starts (light on the pc blinks) but nothing happens. Also my 17.3 linux is intact on the disk. Am using it now. In the isolinux folder on the iso (18.3) file there is a file called vesamenu.c32 26.7kb type unknown. This file on the 17.3 iso had another length and was marked as bin.There doesn't seem to be anything written to the disk. When I started via grub I only saw the 17.3 there. The disk light on the PC during the install never blinks. Any ideas??