As we noted last time, when Tim returns from taking Kit back several years, the child he fathered in the interim has changed from his daughter Posy to a son never named in the film. His Dad probably should have mentioned that, but he has the explanation ready, and it is very definitely a butterfly effect problem: if you change your past even just a bit before you conceive your children, you change the very complex moment in which sperm meets egg forming zygote, such that the genetic makeup of the child is altered. In short, you become the father of someone else instead of the child you know.
It is a simple aspect of the genetic problem in a very logical application, but it raises a lot more questions concerning that same problem. To simplify them, what hypothetically happens if Tim's Dad travels back to a time prior to the conception of Posy? We already know that the actions of time travelers in the past can change the lives of other people--Rupert never found Mary, Kit lives with Jay instead of Jimmy. The problem with butterfly effects is that they involve ripples of change, that one small change in this has a massive impact on that which did not seem to be connected to it at all. We readily accept that the time traveler could return to a future in which his children are different, but could he return to a future in which someone else's children are different?
Obviously it is possible. How many children were born over those few years to people at that party besides himself and Kit (who did not have a child in the original history, but might in this one)? How did that event impact people in their lives--who called her girlfriend to tell her about the fight at the party, so that the girlfriend put her boyfriend off for half an hour and wound up with a daughter instead of a son? Has Posy changed a dozen times outside Tim's knowledge because Dad made trips to the past?
This barely touches on the issues which usually concern us in the genetic problem. Jimmy was dating Kit. We do not know that he was faithful, but we have every reason to believe that were he not dating her he would be seeing someone else. That other girl would be missing whatever relationship she would otherwise have had, and the ripple passes through the world such that dozens, perhaps hundreds, of couples are shuffled within a few short years.
This is a danger that confronts every trip Tim or his Dad makes to the past. The trick is, under the rules portrayed here, only the time traveler himself would be aware of the change--finding that Posy is a boy surprises and confuses Tim, but for Mary the child has always been a boy and she has no idea who Posy might be. Still, it might be wise for Tim to keep a database of the relationships of people he knows and the names of their children--as we saw with the phone number, the memory in the database will be updated to match the changing history even though his own memory never is.
Tim recognizes the difficulty he would have bonding with the boy who is not his daughter, and so makes another trip to the past to fix that. That raises more issues.