Hi Everett,
we have exactly the same error-messages in our error-log. Our settings are: Apache 2.0 Handler, mysql 5.1.49-3~bpo50+1-log, charset utf8, php 5.2.14, PDO-Support: enabled, php_value max_execution_time 120; php_value post_max_size 32M; php_value upload_max_filesize 32M
(ERROR @ /modx/core/xpdo/xpdo.class.php : 1877) PHP warning: json_encode() [<a href='function.json-encode'>function.json-encode</a>]: recursion detected
Btw: We found this error for the first time after activating to APC-Cache but we are not sure if this is really the reason because we changed some link-paths in our template at the same time which also could be responsible.