When newspapers and photographs change in the trilogy to reflect a new timeline, sometimes the change is quick and sometimes it is gradual. In part I, we see Marty's siblings gradually disappear over the course of a week, and at the dance, we see Marty start to disappear. In part III, Marty stops Doc from being shot by Buford, and then Marty accepts a duel with Buford. On the photograph Marty had taken in 1955 of Doc's tombstone, Doc's name had disappeared on the tombstone, but the date (September 7, 1885) and tombstone itself remained.
We see quick changes in part II. In 2015, Marty alters the timeline in a way where Griff and his gang are arrested before his son could participate in a robbery with them. A few minutes after this, Marty and Doc see the newspaper of Marty Jr.'s arrest titled "Youth Jailed" to a story about Griff and his gang getting arrested, titled "Gang Jailed". Toward the end of part II, after Marty burns the almanac, restoring the timeline from the one where Biff was a millionairre, within a minute Marty's sees the printing on the matchbook change from "Pleasure Paradise" to "Auto Detailing", and a newspaper change from "George McFly Murdered" to "George McFly Honored". At the same time Doc sees a newspaper change from "Emmett Brown Committed" to "Emmett Brown Commended". Doc refers to this as the ripple effect. A quick change in part III is after Marty knocks Buford into a wagon of manure, the photograph shows the tombstone disappearing.
Photograph of the Tombstone
In part III, when Doc first observes the photograph after the confrontation with Buford, he says that it makes no sense that the name on the tombstone has erased but the date and tombstone itself still remain. I think it does make sense. If it had Doc's name on it, Doc would have gone into hiding (or found another way to protect himself). If Clint Eastwood's name appeared, Marty would have gone into hiding. If one went into hiding, Buford would have killed the one he could find. This ended up happening after Marty refused to duel against Buford. Marty locked himself inside a building, so Buford told him that if he doesn't come out, he will kill Doc.
Thus, regardless of whose name appeared on the tombstone, a name appearing on the tombsone would have caused the other person's name to appear, so the photo would have to change names. If the names on the tombstone changed, that would change which of Doc or Marty would go into hiding, which would cause the tombstone to change again, so it would change back and forth indefinately like a paradox, so the state of flux would leave .
It may seem like neither Doc nor Marty would have gone into hiding if their name appeared on the photograph, since they could have both gone into hiding but neither did. However, I think they likely would have reacted differently if they had seen their names (or Clint Eastwood's name) on the photograph. If Doc's name appeared, it probably would have frightened Doc that he was still going to be killed even after Marty had already prevented Buford from killing Doc. At least when Marty originally showed Doc the photograph on September 3, Doc thought he would be safe until September 7. After Buford attempted to shoot Doc on September 5, Doc learned that in the previous timeline he took two days to die, and he was in danger earlier than expected. If Doc saw his name on September 6, he wouldn't know when or where Buford would kill him, and he would realize he could not be sure as he previously was, so it would have scared him into hiding.
Marty would have also been scared if he saw Clint Eastwood's name on the tombstone on September 6. Once Clint Eastwood's name actually appeared on the photograph at 7:55am on September 7, it seems clear to me that Marty was scared. I believe this fear is what made him realize the danger in accepting dares to prove he isn't chicken, and why he declined to race Needles after he returned back to 1985.
Photograph of Marty, Linda, and Dave
On November 5, 1955, Doc and Marty observe the photograph of himself with his brother and sister and see that Dave's head had been erased. Clearly the timeline did not alter so that Dave has no head. The photograph thus reflects a combination of two timelines: one where Marty and his siblings were born and a timeline where they were not born.
This case is also a paradoxal state of flux: if Marty and his siblings appeared in the photograph intact, Marty would have believed that his parents would get together without further intervention, and this would prevent Marty and his siblings from being born. If Marty and his siblings had completely vanished, Marty would have intervened and succeeded (as we saw in the film, Marty did get his parents together). Since Marty was going to succeed, a photograph without him and his siblings would be inconsistent with the events of the timeline.
Given the state of flux, the photograph had to remain in a state of limbo until Marty had done everything he needed to do to get his parents back together, since Marty's actions were affected by what appeared on the photograph, and his actions would have changed the photograph.
We see Marty himself start to disappear on the stage at the dance on November 12, 1955, shortly before his parents kiss. I believe the timing of Marty's disappearance is related to when his parents fell in love. The moment Marty's parents kissed marks the point in time after when getting his parents back together would have been impossible, so this is the point when the timeline would have stabilized.
It is curious why Marty stated to disappear at this point. By playing with the band, he was ensuring the dance continued until his parents fell in love, so he was doing what he needed to do. The photograph could not have been fully restored before his parents kissed since that would have led Marty to think he could have left the dance, and the dance would have ended before his parents kissed, which would mean Marty and his siblings were not born and they would disappear in the photograph. However, just because the photo could not be fully restored does not mean Marty should have disappeared. It seems to me that he should not have disappeared until he got to the point where getting his parents back together would have been impossible.
While Marty is collapsing on stage and disappearing, he says George's name. Perhaps George heard Marty, looked over at him and was reminded of his advice, and how following his advice was how George was able to win his fight against Biff and prevent Biff from harassing Lorraine. So perhaps Marty plaing with the band was not enough to get his parents together. Perhaps without starting to disappear, Marty would not have gotten George's attention, and his parents would not have gotten together, causing Marty to disappear. Then the disappearing and collapsing is what caused Marty to call George, which motivated George to be assertive again and get back with Lorraine, which allowed Marty and his siblings to be born.