I am just one of a number of people who are getting this error when trying to update WP or Plugins, and it seems (at least in our case) to be related to our server not being configured with SSL, but our using Curl as the default method of transport.
I added a debug line to wp-includes/update.php prior to the point where this error message appears:
An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration.
Even though we do not have SSL defined, the value of $ssl is set to 1 (true).
According to this thread wordpress.org/support/topic/wp_http_supports-array-ssl-yeilds-true-on-a-local-server WP assumes that SSL is defined if the default transport is Curl, regardless as to whether SSL is active on the server or not.
I am not sure how to resolve this, but hopefully it helps identify the cause of the problem (at least for some people) and gives a clue as to how to fix it.