It really depends on how the framework is implemented. Most javascript frameworks extend the built in JavaScript functions, so that is why you are likely getting conflicts. For instance, many frameworks have a $() function to get a quick reference, but if mootools and yui have that, it will cause errors since both are trying to declare the function and presumably doing it separate ways.
So, my general recommendation would be to stick with a single framework since that will always work.
I don't have any recommendtions for a yui slideshow since I primarily use mootools myself. Hopefully someone else has more experience there.
