Yes there are, but they are minor.
This is exactly the feeling Joseph Heller wanted to provoke. He both intentionally and by 'planned accident' planted anachronisms in the story, and there are some real mistakes as well. The last category is small though, as you noted.
The story takes place during WW2. But it was never intended as 'a realistic novel about WW2'. It was more intended to depict general truths about the madness of bureaucracy. Joseph Heller admits to having little actual war experience, having been overseas for less than a year. Catch-22 was started eight years after the war and written over a period of eight years. Post-war anachronisms in the text abound and were deliberate. Still, the convoluted storyline was carefully designed using note cards and is consistent but for smaller details. It was a first novel, and truly complicated as well.
One inconsistency is about the number of missions over time. Between September 1943 and May 1944 the required number of missions is raised by 10 and Yossarian flies 9. But there is also mention of a number of 6 missions in 6 days in September. Implausible at best.
A comprehensive list together with a chronology:
Spindrift and the Sea: Structural Patterns and Unifying Elements in Catch 22
Clinton S. Burhans, Jr.
Twentieth Century Literature
Vol. 19, No. 4 (Oct., 1973), pp. 239-250