The main mistake I see actors make when performing monologues is that they pick only one emotion and use it throughout the whole monologue.
One example is with the monologue called Demons: http://www.freedrama.net/demons.html
When I had actors try this, several selected one sad or angry emotion and used it throughout which made it a boring performance. The best performances were the ones who selected different types of emotions for different parts of the script. Even though the whole monologue is sad, there are elements of anger, fear, hurting, desperation, madness and even love. The actors that found different emotions to use in different parts were the most interesting and enjoyable to listen to.
Check out some free monologues and try this out: http://www.freedrama.net/small1.html