I regret publishing a sloppy conference paper I have published two conference papers at one conference in physics with two other authors and I am the first author in both articles. And I am currently in the second year of my PhD Thesis and these were my first published papers at all.

I have trouble with one of those articles and I am constantly thinking about it. The positive thing about this paper (as well as for the second) is, that it is very interesting for my scientific community and also for the authorities for decision making about a political charged topic. I used a fancy method and the results are good. 

Firstly, I was satisfied with this paper. I thought it its "just" a conference paper and spending to much time for writing, wouldn't pay off, because this paper doesn't even count for my PhD-Thesis. So, all in all I was very happy with presenting it at this conference. 

The bad thing is, that I was very stressed, when I wrote it. The statistical analysis took a long time and I had not much time, due to caring for my newborn child. I finished writing and correcting this paper (with the other authors) shortly before submitting it. After the reviewer mentioned a very small revision (a more detailed abstract, spelling error or a hint for a better literature reference), I recognized that three sentences within the results had to be changed and also two or three sentences within the discussion. I fixed it, showed it to my supervisor (I don't know how carefully he read it) and now it is published.

After reading it again after some time and very often, I found some mistakes, especially in the parts which I fixed lately after the revision. At first I didn't realized them, but after reading it again and again, I found more and more: A typo as well as at least three grammar mistakes, which are in my opinion not that bad and I only recognized them by reading it a lot (two of them are even in the abstract), but that doesn't makes it better (I don't have an eye for grammar). In the corrected sentences in the discussion I partially used wordings which are more common to say, but uncommon to write in science. Because its my first publication I was more focused on writing things correctly, but after asking other people, I now think, that it is not so handsome and sloppy. There are some other sloppy wordings in other parts of the paper, but I think its not that big of a problem due to the proofreaders didn't complain, but the sum of the mistakes makes me feel very bad about this paper.

Another point is the discussion: The results are great, but the discussion could have been way more precise with a better interpretation, less focus on repeating the results and a stronger focus on other literature. After rethinking it, I would have done it quite differently. 

All in all I regret publishing this paper and I fear that I am in my scientific community now known for bad writing style. And another problem is, it is forever available by Google Search and it could have a significant negative influence on my career, because everybody who writes my name in Google search, will find it very easily. I think many people don't differentiate between conference papers and journal papers.

Has anybody been in a similar situation or can you give me any advice for dealing with it? I think an errata for grammar mistakes wouldn't be justifiable.

By the way: The second conference paper has got a better style.
There is one very easy answer to your problem.

Relax. Do nothing. It's fine.

Really. Your data is good, your results are interesting, people are reading your work, and you haven't found anything particularly wrong with your science. This is more than most of us can say about our first forays into publishing.

That being said, maybe you should work on how much you let small problems get to you if you want to survive in academia. If grammar errors and awkward formulations in a published paper already make you be unable to sleep, I worry that the real setbacks that characterise academic work (experiments that are not working out, unjustly rejected papers, dozens and dozens of faculty applications that you never hear back on, ...) will do to you.