Some downloads give repeated messages in the form of:-

[flv @ 027507e0] negative cts, previous timestamps might be wrongte=3570.9kbits/s

There don't seem to be any problems in the final video, but I am wondering what causes this and whay is the potential significance.

Usually has no significance - just a glitch in the file production, e.g., bad edit or live stream that wasn't re-encoded.

Could also be due to discontinuities in output created when resuming failed downloads. Since you didn't bother to provide an example, can only guess.

I've found this always happens when downloading too soon after the programme has aired but wait a few hours and it generally sorts itself out and downloads properly.