Gov. Ron DeSantis of Florida announced his presidential bid on Wednesday night in a livestream on Twitter that was delayed by technical difficulties and peppered with occasionally misleading claims.

Here’s a fact check of some of his claims.

What WAS Said

“Biden’s also politicized the military and caused recruiting to plummet.”

This lacks evidence. Military leaders have recently warned that several branches of the armed forces are struggling to meet recruiting targets, but the reasons they have cited have little to do with President Biden. Namely, many younger Americans simply fail to qualify.

A 2020 Pentagon study found that just 23 percent of 17- to 24-year-olds can meet service standards, with many failing the military’s entrance exams or fitness and mental tests. That rate decreased by 6 percent from the previous study in 2017.

Army leaders addressed recruiting issues in a congressional hearing in April, noting that the issue has been ongoing.

“The difficult recruiting landscape we face didn’t happen in a year, and it’s going to take us more than a year to turn this around,” said Christine Wormuth, the secretary of the army.

Ms. Wormuth also noted that a Pentagon survey of 2,400 people ages 16 to 28 had asked about obstacles to enlisting. Respondents cited fear of injury and death as the top concern while cultural and political issues — “wokeness in the military or the Covid vaccine mandate, for example — those were relatively low on the list of barriers to service,” she said.

What WAS Said

“In Florida, our crime rate is at a 50-year low. You look at the top 25 cities for crime in America, Florida does not rank amongst the top 25.”

This is largely true. The state’s crime rate did fall to a 50-year low in 2021, but Mr. DeSantis omits a big caveat: Many law enforcement agencies in the state switched to a different reporting methodology and the data is provisional and incomplete in many cases, The Tampa Bay Times reported.

Data from just 59 percent of Florida agencies covering 57.5 percent of the population was used for the state’s total aggregate crime rate in 2021. That mirrors a nationwide trend: Across the country, nearly 40 percent of law enforcement agencies failed to report 2021 crime data because of the new methodology.

No Florida city ranked near the top for violent crime rate compiled by private companies and news outlets. But it’s worth noting the Federal Bureau of Investigation and criminal justice experts have also long advised against comparing crime rates across cities, given the wide variation in population size and demographics.

What WAS Said

“Nobody probably has made Disney more money than me because they were open during Covid. And they were closed in California and that went on for many, many months where literally, I had all the theme parks in Florida opened in 2020.”

This is exaggerated. Disney World in Florida closed on March 15, 2020, along with every other Disney theme park worldwide. It reopened in July, after being shut down for four months. Disney resorts in Paris, Shanghai, Hong Kong and Tokyo also reopened in 2020 after being closed for months. Disneyland in California reopened April 30, 2021, after a yearlong shutdown, the longest among the Disney resorts, once the state allowed theme parks to welcome back visitors.

Mr. DeSantis is also downplaying his own actions during the coronavirus pandemic. He issued an executive order on April 1, 2020, directing all residents in Florida to “limit their movements and personal interactions outside of their home to only those necessary.” While the order did not explicitly close theme parks, it limited openings to essential services and activities, and prohibited gatherings of more than 10 people. The order expired on May 1.

What WAS Said

“The whole book ban thing is a hoax. There’s not been a single book banned in the state of Florida. You can go buy or use whatever book you want.”

This is misleading. There has been no statewide ban of a book, but Mr. DeSantis is vastly playing down the extent to which individual school districts and libraries in parts of the state have removed books. In fact, Florida ranks second, behind Texas, as the state with the most bans at 357, according to PEN America, a nonprofit that supports free expression.

Legislation signed by Mr. DeSantis limiting discussion of sexual orientation, gender identity and race has led teachers and administrations to remove books.

Books that have been removed from shelves in Florida include a picture book about two male penguins raising a chick, Toni Morrison’s “The Bluest Eye” and Margaret Atwood’s “The Handmaid’s Tale.”