Besides the obvious fact that debug messages cannot be displayed in a application that is already in production, and also the fact that I don't know why would you like that, there a couple of things really bad about it.
The first one is that when you add debugging behavior to your server, the debug engine "attaches" to the PHP process and receive messages of the engine to stop at breakpoints, and this is BAD, because introduces a high performance blow to have another process stopping or "retaining" the PHP parser.
Another big issue is that when a debugger is installed, at least most of them, they tend to have the nasty habit of opening ports in your server, because they are not intended for production environments, and as you may know, any software that opens ports in your server is opening a door for any hacker around.
If you need to have debugging in your code, then in your application, implement a debugging system, if is not available, since most frameworks have this built in. Set a configuration value, say DEBUG_ENABLED and when throwing exceptions, if is not enabled, redirect to a petty page, else to a ugly page with debugging information, but take good care of what debugging information you display in your server.
I hope this clarifies everything.
EDIT As apparently my response is not documented enough, you should check these sources
Finally, there is one thing I didn't said as I thought it was sort of implicit: It's common sense not do it! You don't put debugging instruments on your production server for the same reason that you keep them on a different environment, because you need to keep unnecessary stuff away from it. Any process running on a server, no matter how light it is, will impact your performance.
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