It's always better to regret something you have done than something you haven't. I often know what I might squirm a bit about in each of my issues, in the next issue it's publishing my sperm test results.
I have this problem. (Commenting as a writer of personal zines). The zines that I put out when I was 16 now make me cringe eight years later, partly the content and opinions I expressed, but more the style I wrote in. But I try to take the approach that I was happy with it when I put it out, and that's what counts.
It's harder when the problem is more immediate, that as soon as it is written (either immediately after publishing it, or even before that stage) you wish you had put it differently, more eloquently, spent more time on it, thought it through more. The best piece of advice I was ever given on this (given to a friend by her dissertation tutor, then passed on to me) was "don't get it right, get it written". It's better to write it and put it out than spend so long deliberating over something that you never actually put it down on paper, or put it to print. That's paralysis for fear of not being good enough and it's made the most recent issue of my perzine two years in the making and still unfinished!
I'm proud that each zine I have put out exists, and that they are representative of what I felt at the time, even if I might write them differently if I was starting them now. People change over time, and perzines are always going to be a snapshot of how you were at a particular point. Sometimes it's helpful to set yourself a deadline, either a point in time, or a number of pages and just tell yourself that is when you will stop re-hashing and just call it a finished zine. But that won't work for everyone. Try not to be too hard on yourself, and don't strive for an unobtainable level of perfection!
The third issue of my mental health zine functionally ill I was so shaky about, I didn't even put my name on it. I was so afraid it was no good. Then I ended up getting some great feedback on it, and I like it now. So when I felt scared about issue four, I put my name on it anyway because I knew my fears were probably unfounded. I think it's natural to be nervous, and like others are saying, at some point you just have to release it into the world and hope for the best.
as mentioned in another forum discussion about first zines, i'm totally embarassed of just about every zine i've made up until "motor city kitty" number four or so? and even still i know there are ways parts of issue four and six could have been better written and less like a blog/diary. and even things i'd change about issues seven up til ten, the latest. i've had issue eleven sitting since july waiting for its split-counterpart to arrive and the longer it sits, the more i want to edit it!
but that forum discussion got me looking back at ALL of my old zines (which is about 30+) and reading them chronologically and i really love that i have this way to place myself back into a moment of time in my life. there are things in these zines i've forgotten about entirely! its crazy to return to it, even through my mediocre writing.
so like everyone else said, just do it. i think the embarrassment of your first zine is part of the fun- an experience we all go through. its like an initiation. and an artist is always their own harshest critic, right? you gotta just get it out there, and you'll learn with time how to improve.
I´m a bit of ashamed of the Rock / Underground zines i wrote some years ago. some bands that at time i said that was marvelous, now i don´t think it so great. and some band that i really destroyed in my reviews, some time after i even liked it.
in comics zines, no, for me all was perfect. i express there everything I felt at moment, and for me comics are a bit of forever thing, even now it´s a great story, and wil ever be. if i didn´t like the story at time, now it´s still sad for me.