This bug was manageable previously: it happened only rarely, and you could delete the Optical Flow folders inside the Final Cut Pro cache bundle (with the app closed) to force Final Cut Pro to reanalyze the affected clips. You may have had to Render All, click on every retimed segment, or force a Render on each of them, but everything would eventually analyze, and that warning would no longer pop up.
Since upgrading to Final Cut Pro 12, I encounter this issue on every single project that uses Optical Flow (“Best” / Machine Learning), and none of the workarounds above have worked. Worse, I now experience severe artifacting in many of my clips, with flashing images at various points of the retimed segments.
There doesn’t seem to be any pattern to it, with 3-minute clips playing back just fine after the export despite the “background tasks” warning. On the other hand, some 20-second videos are severely affected, exhibiting very jittery playback of the exported file.
I’m going to submit a sample project to Apple, but in the meantime, traditional Optical Flow (“Better” / non-Machine Learning) seems unaffected, at least on the projects I’ve tested. If your project doesn’t need the benefits of the Machine Learning algorithm (eg. occlusion detection), you could try that.