The events that occur in the finale are not unrealistic... life is "messy". The main problem is that it is a lot of stuff to be crammed into 44 minutes of air time.
The second problem (which is partially related to the first one) seems to be that the writers and producers weren't sure how the audience would receive Cristin Milioti as The Mother, so they tried to maintain focus on the big five for most of the season. Of course, in hindsight, Milioti was wonderful and Tracy was written very well.
The third problem (and this is also partially related to the first one) is the mood whiplash induced by the final scene with Ted's kids, which was filmed way back in season 2. After a montage of photos of Ted and Tracy living happily together, overlapped with bits of their wedding, and finally meeting while Future Ted narrates how he is eternally grateful that he had met her... Ted's kids kind of laugh it off with a "that's it?" It almost seems that ending was filmed more with an intention that Ted had a failed marriage with one of his many girlfriends and that he had not dated for 6 years... which is more in line with the early seasons.
Ted's kids encouraging Ted to give Robin one last shot after 6 years of mourning Tracy isn't a bad thing in itself, but it needed to be a more serious and somber moment than what we got. Ending with the blue horn scene after a more serious and somber encouragement would have been a sufficiently hopeful ending.