I think that the most important things for you to know regarding C is the differences between C and C++. You will likely see some code that has some C style in it at some point, and you should not be confused when you see things like malloc, free, printf, fopen, or fclose. You should also know how these are similar as well as how they are different from their C++ counterparts.
You should also know that << and >> are left and right shift operators, not insertion operators. In C++, where you can overload operators, these have been overloaded to perform stream insertion and similar things, but they are still used to shift integers.
Make sure you understand all of the basic features that C++ has that are not in C. If you read stackoverflow.com enough you will have seen many many questions that involve the differences in the languages and people's misunderstandings of them.
You should also familiarize yourself with the C preprocessor, which is almost the same as (and often the same program as) the C++ preprocessor. Knowing how to use it will help you in C++, but it is relied upon a lot more in C.
One big thing that is difficult to deal with in C that C++ has is destructors. Those things can be called all over the place taking care of resource freeing, but in C you have to do all of that more explicitly. This is easy for C++ programmers to forget about doing.
As far as interviews to, if someone asks you to write code for some general algorithm in C and you do something like:
struct foo {
int a;
void * b;
};
foo x; // in C++ this would work, but in C it would fail because struct names aren't in the
// type name table unless you put them there with typedef
I don't think that they are going to decide that you don't know what you are doing because you didn't do:
struct foo x;
And they really shouldn't care if you used cout unless what they are trying to get you to showcase is your ability to deal with input and output, which C++ makes easier for common cases.
If you do find yourself in the position of being interviewed for a job that requires C you should be upfront about your lack of knowledge of C outside of its overlap with C++. They will likely understand that a good programmer should be able to make the transition to C from C++ fairly quickly.
All of that being said, C is not that big of a language. The standard library is much smaller than C++'s and it isn't that big of a deal to familiarize yourself with the most common pieces of it, so it really can't hurt to learn it.
