Hello. I do believe you are referring to disagreements about what exactly happened during Andrew Jackson's First Inauguration? If not please advise and I will correct my answer.
The Inauguration was held on March 4, 1829 at the US Capitol. There was a very large crowd of 10 thousand people, including many Jackson's supporters. After it, he went on horseback to the White House for the Reception. Both Supporters and Critics agreed that there were lots of people and that authorities lost control of the crowd and that all these people stormed the White House and caused material damage and that they only left when punch and ice creams were taken to the lawn outside to lure the crowd out.
However, they disagree about the extent of the damages and the gravity of what happened. Jackson's supporters only spoke of minor, trivial damages and focused on the positive aspects (the presence of so many Jackson's supporters and their loyalty to him) and the press also reported minor damages. Jackson's critics focused on the exact opposite: they stated that the damages were enormous and that the mob was completely out of control. One possible reason is that the crowd was made up of both Jackson's supporters and upper-class Washingtonians who disliked and feared Jackson's policies in favor of lower class Americans as well as these lower-class Americans themselves. Thus, they did have a political reason to exaggerate the damages, the size and the behavior of the crowd.