I'm such a sucker for stuff like this.
I spent almost an entire year at York University studying the intricacies of voice, text, and speech sounds in the service of theatrical performance. One of the most important and challenging part of my studies was the exploration of accent and dialect patterns. We spent significant amounts of time practicing the most effective ways to dissect and reproduce any given dialect or accent, with a substantial emphasis on using the International Phonetic Alphabet. In fact, there is a wonderful book by co-authors Edda Sharpe and Jan Haydn Rowles called How to Do Accents (See here.) that serves as a easy-to-use guide on the journey towards playing new dialects. In the book, Rowles and Sharpe emphasize the importance of finding the sensory and rhythmic aspects of a new dialect and using them as the foundation around which the dialect is built. Mr. Meskimen's here is a fantastic illustration of someone who's employed these aspects to delightful effect.
The most amazing thing about this video is how Jim is able to use the rhythms and idiosyncrasies of each new impression to continue the argument and story of the text. Playing Shakespeare's work is already difficult enough without having to change dialects mid-thought. Somehow, as absurd as it seems, the transition between Droopy Dog (This guy.) and Morgan Freeman (This guy.) seems almost natural and organic.
I listened to the clip once through while following the text he used and it's true he missed and/or paraphrases some bits, but the sense of it is all there. And considering he played in 25 different dialects, I think I'll cut him some slack.