The pseudocode + example given for the initial implementation of 'insert' doesn't seem right, no 'below' connection is made between the two '13' nodes.

The way to fix this would be to let 'insert' return the node inserted at the given level. There already are a few returns in the 'insert' pseudocode right now, but it doesn't seem like anything is being returned right now.

Something like this:

    -- Recursive skip list insertion function.    
    define insert(elem, root, height, level):
        if right of root < elem:
            return insert(elem, right of root, height, level)
        else:
            if level = 0:
                new ← makenode elem
                old ← right of root
                right of root ← new
                right of elem ← old
                return new
            else:
                if level ≤ height:
                    new ← makenode elem
                    old ← right of root
                    right of root ← new
                    right of elem ← old
                    below new ← insert(elem, below root, height, level - 1)
                    return new
                else:
                    return insert(elem, below root, height, level - 1)

Or more simply:

    define insert(elem, root, height, level):
        if right of root < elem:
            return insert(elem, right of root, height, level)
        elif level > height:
            return insert(elem, below root, height, level - 1)
        else:
            new ← makenode elem
            old ← right of root
            right of root ← new
            right of elem ← old
            if level > 0:
                below new ← insert(elem, below root, height, level - 1)
            return new