In the final cut of the film, it seems clear that Phillip Jeffries's sudden appearance in Philadelphia occurs during the course of the Teresa Banks murder investigation (we hear Albert say after Jeffries disappears again that also, "Agent Chester Desmond has disappeared.") We know this is about year before Laura Palmer's murder, so the date would then be February 16, 1988. 

In the Missing Pieces version of the scene, Phillip Jeffries, disoriented, looks at the calendar on Gordon Cole's desk and confusingly says, "1989?" before he disappears. So in this version, the date is February 16, 1989. That is also the precise date that Laura's story begins in FWWM, when she walks to school with Donna.

To me, this seems like they had an issue in post-production, where the editing on film didn't quite work as well in the written chronological order, since we then have Cooper go investigate Desmond's disappearance following the Jeffries incident. If this was chronological, the first time we see Cooper would be him investigating in the Fat Trout Trailer Park. But it flows better into Laura's story when we end on him pondering the mystery in his tape to Diane.

But at the same time, I like the symmetry of Cooper's dream coming true and Jeffries's appearance aligning exactly with the start of the last 7 days of Laura's life.

What year makes better sense to you?