When Frances meets Marcello, she is being pursued by a group of men. As she runs around a corner, her boots are visible underneath her dress and they are medium brown or tan. Later on that same day, when Frances and Marcello start making love in the antiques store, her boots are black.
When Patti is lying on the bed in Frances' house, she is lying on her left side with a pillow under her head. In the next shot, she's lying supine, then reaches for the pillow to turn on her left side.
When Francesca goes to Positano to surprise Marcello, she rides up the winding roads on the back of a Police motor scooter. As they make a sharp right turn, we see an unobstructed view of a miniature village scene in the wall at that turn. A moment later when the camera angle changes, all of a sudden a parked blue truck appears, along with an attentive worker standing behind it.
Near the end of the movie, as a voiceover speaks of the Semmering Pass railway from Austria to Italy, we are shown a train of the Rhätische Bahn (or Rhaetian Railway). Except for a very short section in Italy, the RhB operates only in Switzerland; it's nowhere near the Semmering Pass.
When Frances returns to Positano to meet with Marcello, she is at sea-level. Most (if not all) busses to Positano come in from the hillside as most of the city is almost vertical along the cliffside. She would not have entered the city from the bottom and then climb, she would have to come in from the top and go down.
Contrary to what was previously reported as an error in geography, the domed church shown in the movie is not Santa Maria della Consolazione near Todi. Rather, the church is Madonna di San Biagio, which is located in the valley just west of Montepulciano. Most of the movie is filmed in the area in and around Montepulciano and Pienza. Very little is in Cortona and nothing seems to be from Todi.