There is nothing incorrect about multiple declarations, but the syntax can become confusing when declaring pointers or arrays:

    char *s = "foo", *t = "bar";

A beginner might forget to add the asterisk in `*t` (especially if the first declaration is written `char*` with no space on the left of the asterisk). Similarly with multiple types:

    char *p = "foo", **q = &p, *z[2] = {"foo", "bar"}, *(*f)(const char*) = strdup;

This is correct and an intermediate C programmer won't have too much trouble parsing these, but in the interest of clarity, it makes sense to put each declaration on a separate line.

If you find yourself needing a lot of local variables, that's often a bad sign anyway, since it implies that the function has a lot of state to manage. In that case, you might want to rethink your implementation to make it less complex, or restructure the code to make it more managable.