Steve. Thanks for the reply and some reassurance. What exactly does verification do? And does the quality of the drive have any effect?

Verification = Error Checking
I agree, ImgBurn is the most robust burning application.

I would use imgburn but the download is full of adware and I'm not risking all that hastle so I went for Nero.

Imgburn download used to be fairly clean. You can deny the adware installs, but you have to do it carefully. I use Imgburn for all DVD and Bluray projects.

"Full of" adware?
No, there are two that can expressly be bypassed.

Verification is a test that must pass for a reliable disc, but a pass is not a guarantee that the disc will play without errors on another player. As they say, it is a necessary but not sufficient test.

Another test you can do, with similar caveat, is to buy a Lite-ON burner or similar one with the necessary features, and use the free Nero DiscSpeed to check for Disc Quality. If your burner does not have the necessary features, the Disc Quality tab will be missing. Optical discs use redundancy and error correction, but this is unseen to the normal user. DiscSpeed is able to display the errors before correction. Presumably, a disc with low soft errors now will last longer than one with higher soft errors, because the errors gradually creep up as the disc ages. It also would give more margin when the disc is played on another player which perhaps has a weak laser or more mechanical inaccuracy.

I use a rule of thumb that single layer discs should have a Quality score above 90%, PI Error max less than say 20 and PI Failures no more than say 4. These are arbitrary values, not hard and fast. Once again, good scores here are no guarantee that discs will play elsewhere. Dual layer discs often have higher errors in the second layer, and many people don't use dual layer if reliability and/or universal playability is important.

Buy a good disc brand is probably more useful than anything. I have had cheap brand CDs (not DVDs) that passed similar tests to the above but would not play on a few recipients' players. I would caution against the purchase of the once king, Taiyo Yuden. They are discontinuing (or have discontinued) manufacturing discs and I suspect culled batches are now surfacing. Once again this is my experience with CDs, not DVDs. I have found Verbatim to be reliable, although in the early days I bought some Verbatim packaged DVD-Rs that were actually made by CMC Magnetics. I think Verbatim only made DVD+Rs at that time. In my experience, CMC Magnetics CDs are quite good and good value, but discs are often not identified by the true manufacturer on the package.

PeterDukes's last post above is filled with a great amount of wisdom gained from experience.
I would just add that there are other QA tests that include CRC check verification that can report the possibility of a disc passing muster.
These tests in their design are actually different for the CD, DVD, and Blu-ray burned media so each system must have its own battery of QA.

By now, you may conclude that achieving QA for burn one-offs is more work than just being at the task of the burn itself. AND that is correct! I spend THE time on archival recorded disks, but it would be questionable to do so for a distribution run where you just want to crank cheap copies.