The most in spirit example I have is the way the menu frame worked in Valkyria Chronicles, the gameplay was great, the story (incredibly) was great and the characters were good, but the greatness of the cutscenes showed up how annoying it was to have to click on each cutscene and watch it in small bits(I'm not sure but I've always believed it was probably started off as PSP game) and navigating to the upgrades was just a plain frustration
In To The Moon, the story was unbelievably good, but it had this weird way of presenting it, acting as though there well thought out plot was a twist that just spoiled it slightly. And there was one line that called it's own ending cheesy, which was a bad moment because the story was so good and enjoyable it was immersion wrenching and irritating to her it called cheesy.
The makers of To The Moon also made a freeware heavily story focused RPG called Quintessence
http://freebirdgames.com/games/quintessence/
And the characterisation and complication is mindblowing. I was worried To The Moon was a one off, because it's greatness comes from the interesting choice of character and circumstance, and you can only have an autistic wife once, but Quintessence settled that by coming up with interesting situation after situation...
but it this awkward habit of flashing back (sometimes to events in the same cutscene) to show what a character is thinking. But these characters are fascinating and incredibly well written, we already know what they're thinking! It gets even worse when one of the protagonists does an understandably but incredibly destructive thing to another one of the protagonists, and afterwards there's all these moments when you're questioning whether it was that act which was causing the current events... and then it would flash back to straight up tell you. The game is so good, but it's good in spite of itself
In The Company of Myself
http://www.kongregate.com/games/2DArray/the-company-of-myself?acomplete=in+the+company+o
Uses an incredibly powerful moment of gameplay as story, buts has this slightly overcomplicated necessary bit at the end
From there on the games I really consider good all have pretty well known problems.
FFX- Tidus and Yuna's voice acting
Metal Gear Solid 2 and 4 - We all know it's the cutscenes, but it's a specific point in every cutscene. It's good and fine and interesting and then there's this recognisable moment where everything stops and they exposit something we really don't need to know for ages. It even happens with the end of 4. There's an amazing ending and then suddenly there's more cutscene and they add on a load more exposition that undoes a lot of the goodness.
Metal Gear Solid 3 - Slow start, escort mission towards end