The Uncomfortable Part

Conventions are also a place where the base and sometimes further right or left elements of a party can air their grievances. Though it's often an uncomfortable juncture for the candidates and the establishment both major parties allow a measure of this at their conventions. In 1992 when Pro life Pennsylvania Governor Casey was refused a speech at the Democratic Convention it nearly offset the Democrat's "perfect" convention and subsequent conventions have been executed with more sensitivity.
In retrospect Patrick Buchanan's speech to the 1992 Republican convention is still as belligerent as it may have been then. Still Buchanan's speech may have enabled otherwise indifferent conservatives to support the Bush campaign. Party leaders may push to have theses uncomfortable speeches set aside for a less important time, say outside the prime time. Oddly, Ron Paul was not given time to speak at the last Republican convention, and he may not have even asked for one.
During the 2000 Republican convention, the party faced its own 'Casey Moment' when openly gay congressman Jim Kolbe addressed the delegation. Surprising some, most of the Texas delegation bowed their head during their speech in opposition to Kolbe's homosexuality. While the move did upset some moderates, some believed the move was orchestrated to reinforce Texan George W. Bush's conservative support.
From time to time conventions will allow for a some colorful characters and even a bit of acrimony if it means keeping the party united.