You're getting this error because there are more than one kind of array which you can use in Unity, and they each have different functions and features.

There are built-in arrays, which are fixed-size, and don't have functions which would change their length (like Add, Remove). Built-in arrays are declared using square brackets.

There is also Unity's Javascript Array class, which does have these features - however none of Unity's functions which return collections of objects return Javascript Array objects, they all return built-in arrays!

(there are also many other array-like types available to use, but that's a different topic!)

So if you need to add or remove objects from your collection, generally you would retrieve the built-in array from your unity function, and convert it to a Javascript Array immediately after, like this:

var nodes : Array;
var tagName: String; // tag to find objects

function Start() 
{
    // get fixed array of node objects, store in a temp var:
    var nodesFixedArray = GameObject.FindGameObjectsWithTag(tagName);

    // convert to dynamic array
    nodes = new Array(nodesFixedArray);

    // now we can add/remove!
    nodes.RemoveAt(1);
}

That's not possible, but you can convert built-in arrays to dynamic arrays like this:

nodesArray = new Array(nodes);

and back to static arrays like this:

nodes = nodesArray.ToBuiltin(GameObject);