Musk reached the agreement with the SEC late last week to settle charges in connection with an Aug. 7 tweet about taking the company private.
As part of the settlement, Musk will pay a civil penalty of $20 million and give up his role as chairman for at least three years. Tesla also was fined $20 million and is expected to appoint two new independent directors to the board, as well as institute governance changes.
However, the agreement hit a snag on Thursday after the federal judge assigned to approve it asked the parties to justify the settlement.
Pitt said it's entirely possible the judge may ask Tesla attorneys exactly how they intend to control Musk's tweets.
"This is now a real issue for the judge," he said.
The Tesla board is also going to have to deal with Musk's erratic behavior in general. In addition to his tweets, the CEO gave a bizarre interview to The New York Times and appeared to smoke pot and drink whiskey during a podcast with comedian Joe Rogan.
Pitt said Musk's latest tweet on the SEC riles up investors and makes them "worry about the rationality of the person who is supposed to be running this company."
"His tweets are precipitous, mercurial and dangerous [but] … it's up to the board to try and figure out how they can cabin these impulses he seems to have while making use of his creative genius," he said.
Shares of Tesla fell on Friday morning in light of the tweet and dropped further following news that hedge-fund manager David Einhorn wrote in a note, "Like Lehman, we think the deception is about to catch up to TSLA." Einhorn is short Tesla, which was down almost 7 percent in afternoon trading.
Tesla did not immediately respond to a request for comment
— CNBC's Javier David and Robert Ferris contributed to this report.