At Lake Placid, when Jeff and Ann try to pick up David in the snow, his hat falls off. When the shot changes to behind Jeff, David's hat is back on.
When Ann poured the second glass of whiskey for Jeff, there was about two fingers' worth in the glass; as the scene cuts to Jeff gulping it down, the glass contains at least four fingers of whiskey.
The position of the fur blanket on Ann during the sleigh ride changes several times between shots.
When David is gurgling whilst pretending to be ill, he tilts his head towards Jeff twice in subsequent shots.
When the parachute ride is rising, it is rocking from side to side but the shots of the crowd show it steady. When it gets stuck, the parachute is still rocking but now the crowd shots reflect this.
Because the Smiths entered into the marriage in good faith and were unaware at the time that the marriage was invalid, their marriage is, in fact, still legal under American law.
After first arriving at the cabin at Lake Placid, Ann picks up a handful of "snow" and rubs it all over her face. All the snow falls off her face, which doesn't show even a drop of moisture. If it were truly cold enough (as it can be in Lake Placid) that Ann's body heat wouldn't melt even a bit of the snow, then Ann and Jeff would not have been lingering outside, especially with their coats were unbuttoned.
Mr. Deever explains to David that the reason he is not married is that that Beecham (where he was married) is separated from Brender County in Idaho by the Bass River and really belongs to Nevada. BUT the border between Nevada and Idaho is a straight line and has NO natural geographical features, such as a river.