A bit too late (like a year or so, but just stumbled on this video preparing for my own interview...). Anyway here is my 2 cents in Java (handles case, punctuation, spaces by ignoring them). Tried to compress the algorithm as much as possible, but still keep the readability:

    public static boolean findPolyndrom(String polynd) {

        if (polynd == null || "".equals(polynd = polynd.toLowerCase().trim())) {
            return false;
        }
       
        int index = 0;
        int length = polynd.length();

        char forward = 0;
        char reverse = 0;
       
        boolean isValidString = false;
       
        while (index < length) {
           
            while(!Character.isLetterOrDigit(forward = polynd.charAt(index++))) {
                if (index >= length) {
                    return isValidString;
                }
            }
           
            while(!Character.isLetterOrDigit(reverse = polynd.charAt(--length))) {
                if (length <= index) {
                    return isValidString;
                }
            }

            isValidString = true;
           
            if (forward != reverse) {
                return false;
            }

            if (length <= index) {
                break;
            }
        }
        return true;
    }