There are many example, especially in Deathly Hallows (both the book and the movies), where it is mentioned that using someone else's wand without mastering it will cause problems for the user. The typical consequence given is that using someone else's wand without mastering it first will make you a much less powerful wizard while using it.
Is there any example of a spell not working, or working poorly, because the wizard was using someone else's wand? I'm aware of some instances where a bad wand caused problems, but I'm not aware of any instances where these problems were a result of the wand not being mastered. For example, in Chamber of Secrets, Ron breaks his wand (which he got from his brother Charlie) early in the book, and has to fix it with Spello-tape. The various problems that this wand causes throughout the book are generally attributed to the poor repair job.
The only clear example of this principle that I know of is the Elder Wand, which follows its own, unusually brutal wand mastery rules.