In a Cinematic film being edited in Final Cut Pro 10.8.1 a white dot or dots appear in timeline.

Got it . . . they seem to be connected with auto or manual focusing. These are Apple's instructions.

Change the focus subject in a Cinematic mode video

Camera automatically identifies where to focus while you record in Cinematic mode and can automatically change focus if a new subject is identified. You can also change the focus subject manually.

1. Go to the Photos app  on your iPhone.
2. Open a video you recorded in Cinematic mode, then tap .
3. White dots under the frame viewer indicate where Camera automatically changed the focus while recording. Yellow dots indicate where the focus was manually changed.
4. Play the video, or slide the white vertical bar in the frame viewer, to the point where you want to change the focus.
5. Tap a subject, outlined in yellow, to change the focus; double-tap to set automatic focus tracking on the subject.
6. A yellow dot appears under the frame viewer to indicate the focus was changed.
7. Note: You can also touch and hold the screen to lock the focus at a specific distance from the camera.
8. Repeat the steps above to change focus points throughout the video.
9. To remove a manual focus change, tap the yellow dot under the frame viewer, then tap .
10. Tap Done to save your changes.

Tap  to switch between automatic focus tracking and your manually selected focus points.

After you save your changes, you can revert a Cinematic mode video to the original if you don’t like your edits. Open the video, tap , then tap Revert to Original.

Here's the link . . .

Cinematic Editing

SORRY! I misunderstood what white dots you meant!

I don't know. Nor do I know what all those yellow dots are!

They show that the section with them has not been rendered.

You can ignore them as rendering is generally not needed with a modern Mac.