I partially agree with Wildbow. It is important to move forward. Figuring things out as you go is a huge part of serial writing. Problem solving, as well. This is also an incredibly useful mindset to have when you're not 100% sure about the text you're going to post. Maybe you're uncertain of a rule that you're about to establish or the direction it might lead you, but when you can suddenly say, "Welp! It's posted, so now it's canon! Whatever this leads to, I guess I'll just deal with it!" There's something liberating in that approach, and when the time does eventually come that you have to deal with the consequences of what you hastily wrote in the past, it can be a huge confidence boost when you successfully turn it into something interesting.
That's sort of the nature of serial writing. I do a lot of brainstorming, but I still end up having moments like that. I think it might be unavoidable, unless you just keep a ridiculously large backlog.
However, I do think that rewrites can be useful, especially for the first few chapters. The beginning of the story doesn't need to be amazing, but it should at least mediocre, up to the point where the story really starts to develop and come into its own. Finicky readers might not give a mediocre beginning a proper chance, but you shouldn't worry about them. They can be persuaded by other people's recommendations. Also, they're finicky, so they're jerks.
I would not advise rewriting the beginning just to retcon yourself out of a corner, but I <i>would</i> advise it if you see glaring problems in your old work. I'd also say that it depends on how long you intend to continue writing that same story. If you're going to move on to a new serial in a year or so anyway, then maybe don't worry about rewriting too much.
With that said, I've not done any rewrites on my own serial. I have, however, made a lot of tweaks, which have probably had a cumulative impact that is similar to a rewrite.