Factual error: Shortly after the crash, when Chuck is in the raft, one of the engines continues to run even though it is half submerged in water. The engine would not have exploded like it did, rather, it would have just stopped running as soon as it became disconnected from its fuel source and flooded with water.
Continuity mistake: The final sequence of the film has a whole load of stuff different. Just before Chuck walks into the crossroad, we see there's a solid double yellow line on the main road, a dirt track to one side, and another road on the other side - that one has one solid & one dashed line on it. It cuts to a wider shot, and the dashed line has suddenly become solid, the Texas state sign has moved closer to the stop sign, and a big shadow (of a telegraph pole or similar) has appeared next to the stop sign. There's then another cut looking down the adjoining road - Tom Hanks' shadow's done a complete 180, the shadow of the telegraph pole's disappeared, the line's gone dashed again, and the Texas sign's moved away. Basically, in one 20 second clip at least 4 things change significantly - they used two very similar, but not identical junctions, for no good reason. A veritable spot the difference competition! (02:10:30)
Factual error: On Tom Hanks' doomed flight, there is no smoke curtain or solid bulkhead in place. This is a heavy, opaque curtain or solid wall that separates the the topside cargo area from the seating area, designed to keep smoke from a fire away from the crew. On DC10/MD11 aircraft, this is generally a solid bulkhead, and on Airbuses a curtain. This plane should have been grounded until one was installed.
Other mistake: In the cave we see Tom Hanks drawing an analemma without a precise timekeeper, which is needed to draw one. What he could have done is a meridian rect, which is build with the meridian time. The analemma is the differential chart between the solar time and civil time.