You have seen it referenced many times, the mutinous petition that was signed after Chickamauga, and from many historians you would believe that the list would have been incredibly long. Here are the names that were on the petition,
Jno. C. Brown
R. Lee Gibson
Several things that are interesting to note are who isn't on the list, Bragg detractors such as John Breckinridge and Frank Cheatham stand out. Also, notice who did sign the petition, James Longstreet, Wm. Preston, S.B. Buckner, A. Gracie, and even D.H. Hill are relatively new faces in the Army. Also note that under Cleburne, Smith, Lucius Polk, and Bushrod Johnson had been in the same Division. Johnson having been detached earlier in the summer to Stewart's fledgling Division where John C. Brown was also a brigade commander. Stovall and Gibson were Brigadiers in Breckinridge's division with Gibson having a negative prewar history with Bragg. So even within the list there are a number of connections among these men that voiced their opposition to Bragg.
Finally of note, Generals Gracie, Smith, Johnson, Stovall, and Gibson all had personal problems with Bragg, Johnson and Gibson had prewar history with him, Gracie had been a subject of concern with desertion problems and the rumor of a unionist cell in his brigade, Smith had been on Leonidas Polk's staff and then the Colonel of the 5th Confederate Infantry, and had a problem with Bragg over his rank. So it would seem that for a good portion of the most vocal Anti-Bragg men that they had more of a personel aggenda than merely the wellfare of the army. To be fair, Buckner and Cleburne were both held in high regard by Bragg after Chickamauga who had recommened both of them for promotion. There support of the petition was a shock to Bragg. So when you look at all of these factors a clearer picture of the opposition to Bragg can be seen.