As a class library example (which is contrary to what I said earlier about .NET compatibility vs C# compatibility) is that it was a massive mistake to let double.ToString() use the current culture rather than the invariant culture. It should change to either required passing a culture always (breaking API change) or change to use invariantculture (behaviour change requiring code changes to keep old behavior)
I would imagine that's a carryover from the Win32/Client-Server days when that would have been a better choice.
Is that annoying? Yea. Is that annoying enough to force companies to collectively spend billions to look through their decades old codebases for double.ToString() and add culture arguments? Also keep in mind, this is a runtime issue, so the time to fix would be much more than if it were a compile issue. I would say no.
As a guy who has worked in C# since 2005, a breaking change would make me pretty irate. Backwards compatibility has its benefits.
What issues do you have with backwards compatibility?