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.
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 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.
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.