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.

Conversely...

Lower ballot candidates can make a name for themselves with the conventions. Keynote speeches are often utilized to present a rising star of the party to the American public. Ann Richards 1988 address to the Democratic Convention helped raise her profile for a subsequent run for Texas Governor. New York Governor Mario Cuomo's 1984 appearance at the Democratic Convention made many consider him a good choice for President in later elections. Memorably Barrack Obama's speech raised his profile considerably as a state senator.

The Pitfalls of Conventions

The last real convention, some might say, occurred in 1976 after Gerald Ford beat Ronald Reagan by only 100+ delegates. President Ford had come to the convention with more votes and delegates than Reagan, but neither had a majority and both wooed delegates throughout the convention. Some pundits even thought Reagan, with firmer adherents may upset the President. When all was said and done Ford came out on top. Reagan, maybe purposely, delivered a graceful and much more inspiring address than the awkward President, and Ford was denied a perfect convention from which to launch his candidacy.
This kind of drama was almost recreated in 1980 when Carter and Kennedy battled for the Democratic nomination. Though Carter went into the convention with the nomination sewn up, it was still a contentious affair with a sitting President again being opposed by members of his own party for nomination. The President’s tenuous grip on what should have been his base was epitomized by Kennedy’s very public refusal to shake Carter’s hand following Carters nomination.
Candidates can be disabled by their own selves at these conventions as well. Walter Mondale may have lost any real shot at besting President Reagan saying during his 1984 convention speech that he as President would indeed raise taxes. Bill Clinton’s long winded introduction for Michael Dukakis during the 88’ convention proved an embarrassment for the nascent Arkansas Governor.