I understand a lot of hate the show is getting for how the final part of the story was played out in terms of presentation, but I don't understand the issues with the actual story.
Just for some context, I've only been casually watching the show in re-runs on a channel in the UK mostly showing later seasons stuff and the only season I've followed in full and in order is this last one.
To me, it all seems to make sense. Barney and Robin were a match made in hell. All their characteristics that matched up and made them good together in the moment were the ones that meant they wouldn't last. Barney only "changed" in brief moments of realisation, if at any point the narrative that was centre stage was anything other than him, he was exactly like he'd always been.
Pretty much everything I've seen, including the whole Barney and Robin being together arc, leads to Ted and Robin being together being inevitable. Ted's always been this ridiculous, larger than life romantic who believes in destiny and fate. That doesn't just go away after nearly a decade, even when he finds someone else. Robin will have always been his "What could have been?" whether the mother was alive or not. It doesn't mean he didn't love her, but he'd never be properly over Robin.
Now, things I will take issue with. A whole series set over a weekend, seriously? The pacing for the entire last season is complete sh*t. When you have such a short timeframe stretched out over 22 episodes, you can't just go and cram decades into 40 minutes. Payoffs don't work like that. Iy should have been several episodes at least. The subject matter (friends drifting apart, a mother/wife dying, a marriage ending, having a child with someone you don't know etc.) doesn't lend itself too well to a sitcom, but let's be honest if you're here at season nine you're probably not just tuning in for the sex jokes any more.
My other problem is a bit minor really. I hated how the finale treated Robin. As far as I can tell she's always been dedicated to her career completely. Sh*t, she only met all these people because she moved to a different country to pursue it. She couldn't have kids so it was never going to happen that she meets someone and settles down to raise a family. It was a given that eventually she was going to be on the move again, and the rest of the group, especially Lily, made her out to be a bitch and a bad friend. The only one in that situation who is a bad friend is the one who resents someone for doing what they love. Life happens, people drift apart in geography and personally. Just because they're not available 24/7 for you doesn't make them a bad friend, resenting them for that does.
TL;DR: The plot developments make sense. Having them all occur in about 15 minutes doesn't. Also, Lily's a child.
Side note: My actual name is Robin and I'm a guy. Writing that all out was super weird for me.