It was suggested last time that if Blackadder returns to the same exact moment he previously visited, he would replace himself. It was already shown that he is not the same person, and therefore cannot be said to be the same person who previously visited; but there is also the problem inherent in the idea that arriving at the same moment would mean that his other self would not arrive.
Part of the problem lies in the definition of at the same time. How accurate does that concurrence have to be? Is it sufficient if he arrives to within the nearest hour? That hardly seems to be "the same time". What about the nearest minute? nearest second? nearest nanosecond? When we say he arrives at the same time, do we really mean that there is not the slightest difference by any standard of measure between the two arrival times?
That in itself would be somewhat incredible, given the crude (in the sense of rough and inaccurate) nature of the controls (levers and dials with no markings for relative positions) and the crude (in two senses) means of navigation (what we might call the pearl diver memory technique). The idea that Baldrick could get the controls set correctly to the nearest day boggles the mind; that he hit the same instant by any standard is entirely incredible.
However, if we overlook that, we still have the problem of why simultaneous arrival should be different. We know that if they arrive years before their previous arrival they do not undo their previous arrival; we know that if they arrive years after their previous arrival they do not undo their previous arrival. We can reasonably assume that this would be so if the interval were months, or weeks, or days, or hours. We get down to minutes, and still have no problem imagining both time travel teams arriving, one after the other, possibly interacting with each other as temporal duplicates. From minutes it is a small step to seconds, and from seconds to nanoseconds, picoseconds, perhaps down to yoctoseconds, we are forced to agree that as long as one party arrives incrementally before the other, each should arrive and be distinct time travelers.
What, then, would be the logic of suggesting that if somehow a time traveler arrived at the exact same instant as a previous version of himself, he would replace that previous version? Two people can pass through a door together; two people can enter the same room from different doors at the same moment.
Perhaps it is because they would occupy the same space, and so would merge. Why they should merge instead of colliding and knocking each other out of the way is unanswerable; but then, if we accept that they do merge, why should the older version of the time traveler, that is, the metaphysically second one to arrive, be the controlling mind?
If this is a divergent dimensions story, then everything we learn about how those divergent dimensions work in the first trip is contradicted by the second one. It is internally inconsistent.
Without belaboring the issue, this is also so if we adopt a parallel dimension theory explanation. Some of the problems would be slightly different, but ultimately we face the issue that the events of the first string of travels demand one set of time travel rules, and the events of the second string break those rules completely, so no time travel theory will work to explain all the trips.
Blackadder Back & Forth is a fun and humorous (if sometimes a bit crass) movie, but it is, as anticipated, a time travel fiasco.