Hm, I'm not exactly a coding expert, so I could be wrong. But if they're using Renpy to code their game, there should be no reason for bugs to pop up that break your saves. Unless you're coding wrong. In v0.1, I coded wrong. That's why saves didn't work back then, but I could do almost anything to the code now without breaking a thing (that isn't easily fixable anyway).
I've actually spent all day on Friday cleaning up all of the code, polishing stuff, mainly things the player will never notice, but makes things much easier for me. Which caused many bugs in the latest beta, but it only took 10 minutes to fix it all.
In any case, you could keep your save and just start another save to experience the remade events (Lin's first couple of events were heavily redesigned, so I recommend playing through those the most). Other than that, I think v0.4 more than any other update will feel better if you replay it, but in all honesty, I personally wouldn't. I typically only care about the new stuff in an update.