Our app servers (weblogic) all use log4j to log to the same file on a network share. On top of this we have all web apps in a managed server logging errors to a common erro
Best case I would imagine you have a potential performance problem with sync access to the log file resource. Worst case would be some of the scenarios you mention.
I would ask two Qs: a) what was the desired goal with this config and b) can you find a better technical solution to achieve the goal.
My guess is that you have a sysadmin who wants to get a "single log file for the system." The file is thrown on the network share to make it easy to get to. The better answer for the goal might be multiple files, local to each system and something like http://www.splunk.com/ for a nice monitor.