Other mistake: When Tom Hanks cuts his hand and loses his temper, he picks up the volleyball with a bloody hand and throws it. When he picks it up, you can see that his fingers are spread. When you see the handprint that he makes "Wilson" with, you can see that the fingerprints are together and parallel.
Continuity mistake: After becoming stranded, Chuck discovers the first package to wash ashore. While he is walking towards it, you can clearly see some of the stretch of beach behind him (as well as some in front of him) This shot is somewhat of a tight one. When the camera "seamlessly" cuts back to a shot of him bending over to pick up the package, you can clearly see that the beach is now covered with dozens of jagged rocks. The rocks would have been seen in the shot before this. But in this case, the shoreline was cleared of them in the first shot. (The beach is not cleared of the rocks; they are underwater. Still a good continuity error submission, but caused by filming the shot at high tide and low tide - it is the same section of beach)
Continuity mistake: When Tom Hanks opens the FedEx packages he finds the ice skates. When he decides to cut a bandage for his cut leg he uses the skates to cut the material to wrap his leg. If you look at the skate while he cuts the material there is no shoe tie on it but when he drops the skate to get the shoe tie it is back on it.