<p>is it possible to use the ajaxComplete or ajaxStop features of jQuery to decide whether or not the callback gets called?</p>

<p>Essentially I want to be able to take basic error checking code that is currently in most of my callbacks, and add it to a sort of global callback.</p>

Sort answer: No.
Long answer: Both
```
ajaxComplete
```
and
```
ajaxStop
```
are jQuery AJAX events. You cannot prevent events from happening - and "event" means nothing else as "execute every callback function that has been registered". Callbacks get called regardless, if you want or not.
What you
can
do is program your callback so that it does
nothing
when certain requirements are (or are not) met. In effect this is exactly what you asked for. If you edit your question to explain what you're up to exactly, people can show you how to do it.