I recently tried manually updating to 4.1.1, and received the error to a call to the undefined function wp_json_encode, in wp-includes/update.php. There were 3 lines in setting an array variable, calling the wp_json_encode(). Since, it appears to be a new function call/name, I removed the wp_, and it fixed my one problem, which was getting into my Plugins. I’m wondering if this is an issue with older versions of PHP — we are on 5.2.4. I hope this might help. But, I’m sure this is not an appropriate fix — just a work-around. Maybe, WP can eventually fix or shed some light on this issue. It would be nice to upgrade to the latest PHP, MySQL, etc., but it’s not currently an option.