I want to know if is there a page where I can check if a new update has some bugs or causes problems after the installation.
the first place to look is the homepage:
or the news page to be more specific:
the "news" mostly mentions package updates which will need manual intervention. that means "update problems" that are known and expected. it only covers official packages. that means no AUR packages.
there is also a mailing list which will email you the news items:
the second place to look is the forums:
or directly in the subforum aptly named "Pacman & Package Upgrade Issues":
skim the first page for any obvious update problems. if there are none then you are usually good to go. either that or you will be one of the first to be experiencing the problem. there is no 100% safety.
also the bug page:
but most people tend to post on the forums first and in bug page later, if it has been confirmed to be not a custom configuration problem.
bonus: there is a tool which "enforces good discipline" when updating.
i do not use the tool. it is also already three years since the last update.
To add one minor point to lesmana’s already excellent answer:
I haven’t used it myself; I just ran across it in the Pacnanny README and feel it deserves a mention on its own.