During the beginning credit sequence, Bruno is driving around looking for a public telephone. He finds one locked behind a storefront gate. He pulls out a coin from his pocket and, using his left arm his wristwatch visible, tries to insert the coin into the public telephone but when the closeup shows him trying to insert the coin, it is his right arm that is depositing it and obviously no wristwatch.
When Roberto walks over the rocks, we see a beautiful blonde in a bikini lying on the rocks, reading a magazine and showing her beautiful legs. Later, on the same day, maybe a couple hours later, the same blonde will come and ask Roberto to sign her cast on her leg ("next to Peppino DiCapri's signature"). In the afternoon, she'll be dancing with her cast. It is impossible that the same girl had such a terrible accident that required the whole cast of her leg and then go back dancing with a cast full of signatures (including one by the great Peppino) on the same day.
When Roberto feels sick and Bruno stops the car, Roberto jumps over the closed door, but after the cut the door is suddenly open.
There is an odd shadow on the back of Vittorio Gassman's back in the beach free-standing handstand scene during the close-up. His elbows are never locked. His biceps and triceps muscles do not appear to be under any tension from holding his own body weight up in the air. Someone or something must be holding his legs up unless he has superhuman strength.
The German tourists' MG Roadster has fake German license plates, there are no road test / tax stamps and the GR series doesn't match anything in 1962.
You can see part of the rig on Bruno's car when they talk about Antonioni, when Bruno makes fun of the Italian family on the motorcycle, and when he teases the cyclist.