I think of a thesis as sort of an immature document, by definition. It delineates the university era from the professional era, and is bound to lack some practical elements. Should a student refrain from publishing his or her thesis on the Internet, for this or any other reason?
Every document is, in the way you define it, immature. With everything you write your writing improves. Your papers will not be better because you have a degree. They will be better, because you learned something (i.e. made mistakes) before.
However, there might be reasons not to publish your thesis, but it is not so different from normal working papers. Maybe your thesis is just bad, you did not get any meaningful results, you have made significant mistakes, etc.
So if your university allows, publish it online if you want to (or if you think it may be worth reading / you can not think of a good reason not to); everyone knows, it is only a master's thesis and will read it in a different way than they would read a published paper (or not at all).
Like you say, a thesis is not necessarily as thoroughly peer reviewed as a journal article. In my opinion, that doesn't mean the thesis should not be publicly available, just that a reader should keep in mind that the document is a thesis when reading it and (potentially) citing it. The onus then falls on the reader of a thesis, not on the writer.
In the end, the decision of whether to make your thesis public is more about your university's policy. At the University of Waterloo, for example, all accepted theses are publicly available by default through the same web portal. Other university's have IP policies that may not allow you to publish your thesis (though these policies are rarely enforced).
When the policy is ambiguous or left up to you, I would strongly recommend making it publicly available.
Unless there is a compelling reason not to, yes, you should put your thesis online.
A thesis is supposed to represent your first foray into academic research. The whole point of academic research is to make a contribution to the body of human knowledge, and share it with the academic community. As such, I would encourage you to make it as convenient as possible for the community to read your thesis, and posting it online is a good way to achieve that.
If your discipline uses arXiv or a similar preprint or document server, I would encourage you to post it there as well; that way it will remain accessible even if your web site moves.
I would not worry about your thesis containing "immature" work. It's a thesis; everyone knows that it's your first research product, and nobody is going to judge you harshly in 20 years because your thesis wasn't a work of staggering genius. But on the other hand, they very well might still find it useful. You spent a lot of time writing that thing; don't you want it to be able to do some good?
Also, there's a good chance that your thesis is already publicly accessible (via interlibrary loan from your university, or a commercial thesis database, or something similar). If so, then posting it just saves (possibly a lot of) time and effort for those who want to read it.
Here is a non-exhaustive list of compelling reasons why you might not want to post the thesis.
Your university's intellectual property policies forbid it. (If so, shame on the university. This seems unlikely to me, but some other answers think it's plausible, so I suppose you should check.)
You have submitted parts of your thesis as a paper to a journal / conference / similar outlet, or plan to do so, and the journal's copyright agreement forbids you to post the thesis. (If so, shame on the journal.)
Your thesis contains collaborative work (such as jointly authored papers), and your coauthors object to you posting the thesis. (If so, shame on your coauthors.)
You have published your thesis as a book, or plan to do so. In that case, posting it might hurt sales of the book, and might also be forbidden by your agreement with your publisher.
Your thesis contains ideas of commercial value which are not yet patented, or un-patentable ideas that you plan to exploit commercially. (But as noted above, your thesis may be available to the public already, albeit less conveniently.)
Your thesis contains a serious error that invalidates its results. (But you might still want to post it along with an addendum that explains the error; there may be parts of the thesis that people would still find useful.)
My school, while doing a Master of Advanced Studies (MAS), required a thesis to be publicly available. It only grants exclution to this for commercial reasons, when the thesis is sponsored by a company. However, still, the abstract will be published.
The school provides a search for all Thesis papers, for example here (search is german, but papers are sometimes english):
I like the idea of publishing my thesis, it's a work I am somewhat proud of. I even have a download link on my personal homepage.
If your thesis contains classified material, you obviously cannot put it online. otherwise do it.
You will get feedback and you will get pointed out about good or bad things. This is a standard scientific process and as well a good opportunity for you to optimize your neural network (aka "learning").
If it turns out that your thesis is overly bad, you can still take it offline later. And if someone later still has a copy and asks you why your thesis was so bad, then accept and explain that you know that and learned from it. There is no shame in improving.