In the 50th anniversary special The Day of the Doctor (the only multi-Doctor story in New Who), the following short exchange explains that War and Ten will be unable to remember any of the events of the episode, and only Eleven, the most recent incarnation, will retain memory of them:
WAR DOCTOR: I won't remember this, will I?
11TH DOCTOR: The time streams are out of sync. You can't retain it, no.
10TH DOCTOR: I won't remember either [...]
As well as the necessity of ensuring that Nine and Ten truly believe they destroyed Gallifrey, even in the new version of time (otherwise their entire personalities would have been different), this also neatly takes care of the question of "why doesn't Eleven, the most recent incarnation, simply remember everything that happened in this episode and tell/warn the others?"
Was this same idea of "time streams out of sync" used in the multi-Doctor stories in Old Who? If not, how (if at all) was the issue of memory retention taken care of there? Back then, how did they deal with the issue of the most recent Doctor knowing exactly what was going to happen by virtue of already having the others' memories of the same events?