As stated.... it happens. That is also why they have their copy in hand. Most simply flip to the document they are signing to check numbers and move on.
If a signer is a line item reader you handing him/her/them their copy for reference is not encouraging them to read. They are going to do it anyway.
The point is to not have them handle the copy of the docs I need to walk out with & position myself to pace the signing.
If you find the opposite... don't do it. Their is no definitive how-to for this other than make sure everything is correct by the end of the signing.
Stop letting worry & fear from your 1st experience shade your next few 100 - 1000 or you'll stress yourself out of even wanting to get the experience you need to be more confident in what you do.