There is a huge difference in The Two Towers between loyalty on the Good Side and loyalty (or the total lack of it) on the Bad Side. Loyalty keeps the good people in this book together. But because the people on the Bad Side are, by definition, untrustworthy, they cannot be loyal to each other. Of course Saruman is going to betray Sauron at the first opportunity he gets, because Sauron would not hesitate to hurt Saruman if it could earn him some advantage. That's the problem with being evil: you can't rely on any of your friends.
Boromir's final act of making peace with Aragorn before he passes away is an example of true loyalty, which is the central virtue of the moral of The Two Towers.
The disloyalty among the orcs of Isengard and Mordor just goes to show: Sauron can't triumph, because his troops are always looking out for number one—themselves.