DES MOINES, Iowa—An election debacle unfolded Monday night as the Iowa Democratic Party failed to release the results of the state’s presidential caucuses, saying it had found “inconsistencies in the reporting” as the nation awaited the outcome of the first-in-the-nation nominating contest.

“In addition to the tech systems being used to tabulate results, we are also using photos of results and a paper trail to validate that all results match and ensure that we have confidence and accuracy in the numbers we report,” Mandy McClure,...