Yup, you're right, your DVD writer is playing up. I don't know what OS you have, or even what model/year of Mac Book Pro you have ( I'm assuming it's not too recent, as Apple doesn't put DVD drives in their notebooks anymore. I don't even know how much RAM (memory) you have in it, so my answer will be general. Info on that can be found under "About this Mac" under the big Apple icon at the top left of your screen. You could try using a commercial DVD cleaning disk in the drive or a good shot of compressed air in there. Some brands of DVD's seem to work better than others, eg Verbatim and Taiyo Yuden. sony, and maxell not so much. Also, are you trying to write this to a DVD-R or DVD-RW ?? The first one is un-erasable, the second one mostly is.
You could also try zapping the pram and resetting the SMC/PMU for your model of MacBook Pro. How to do that can be found by using google/yahoo/bing and typing in the name of your mac book pro model & "zap pram" & "reset smc/pmu". It's really easy once you know how to do it. If None of these things i have suggested to you have made any difference at all, eg nothing shows up, doesn't quite copy all the way, then the drive might be dying. Also, apparently there's a bug in Mojave where dvd's don't show up on the desktop, especially blank ones. You can still read and write to them, they just don't show up (don't ask me why, I don't know).
If the dvd drive is indeed dying, then it's time for it to be replaced. Depending on the age of your MacBook Pro, your local apple store can help you out with that, but if it's too old, then you might want to look for an independent aasp (apple authorized service provider) or replace it yourself. Yes: that is entirely possible and do-able. iFixit and macsales.com should have guides on how to do it, what's involved, and they'll probably sell you a new dvd drive to boot. There are other places that'll sell you one, but these are the only 2 that come to mind now
good luck
John B
