What can I do if I find errors in someone's thesis? I was browsing someone's thesis from a US university. I found several typos and missing (incomplete) sections. There was no plagiarism and dishonesty though. What would happen if I write to their advisor? Can some action be taken or is it a closed case once a thesis is accepted and signed.
Generally no official action can or should be taken regarding errors in a dissertation (assuming they are not a sign of dishonesty or fraud).  However, it could be worth pointing out errors to the author in case he/she is preparing a publication based on the dissertation.  I wouldn't do this if it's from long ago or you see that the material is already published, but you could be providing a useful service to the author otherwise.  (If these errors have already made it into publications, then it's worth reporting them to the authors if they are substantive, so they can decide whether to publish errata, but it may not be worth reporting typos.  I'm a perfectionist and would like to know of typos in my publications, but others might be annoyed.)

But you certainly shouldn't write to the advisor.  That comes across like you are reporting bad behavior to an authority figure, so it's not appropriate unless that's the message you want to send (for example, if you discover plagiarism).  Instead, you should communicate directly with the student who wrote the dissertation.  If you can't figure out how to track down the author, then you can assume he/she isn't pursuing a research career and you don't need to worry about it.