In the following example, what are the possible problems that can occur.
id c = [Person alloc];
[c init];
The main problem with the code in your example is that in some cases, the -init method returns an object that's different from the one that you created with +alloc. If that happened, then your code would be incorrect because you're not assigning the result of [c init] to c, and you'd end up working with the wrong object (and one that's not properly initialized at that). This is why the standard idiom is to always combine +alloc and -init on the same line:
id c = [[Person alloc] init];
Now, you may have written the Person class and have first hand knowledge that -init always returns the same object, but I shouldn't have to be intimately familiar with the inner workings of Person to read your code and have a sense of whether it's correct or not. Your code is "better" in the sense that anyone can tell that it's doing the right thing if you follow the usual convention.
I don't think it's horrible to declare c as type id, but it does seem silly in this case. You know that c will be of type Person*, so why declare it as id and throw away useful information that the compiler can use to help you write better code? If there's a good reason to use id, that's fine, but if you can be more specific about the type you should do so.