In the first meadow scene, young Clare pulls off her right shoe and throws it at the bushes, where she believes her brother Mark is hiding. When she runs to take the blanket to Henry, we see that it is her left shoe that is missing off her foot.
In the fireworks scene just before Henry is about to die and Clare is sitting on Henry's lap, when we see her face she is dry-eyed. When the camera shows her face from the back looking at Henry she has clearly been crying, with a tear rolling down her face, and the next shot shows her dry-eyed again.
During one scene Henry talks to a young Clare in the meadow, she is wearing a dark purple t-shirt with a white pinafore dress. In some shots of Clare a white thread/piece of fluff is clearly visible on the dark background of her purple sleeve, it disappears and reappears between shots.
At the ending scene when Claire picks up the cloths Alba picks up the shoes that Henry was just wearing as he walked out of the bushes, the shoes have no laces in the holes. That would make it difficult to walk that long distance across the field.
Why would a wedding band perform "Love Will Tear Us Apart" during the reception? It's a dark song about a disintegrating marriage, and the lyricist's (Ian Curtis of Joy Division) state of mind before committing suicide.
If Henry time-travels nude, he would not have lock picks. However, it is possible to pick locks with paper clips, hairpins, basically a couple of stiff wires. These are not particularly difficult to find.
Henry states at the beginning of the movie that he tried to prevent the car accident that killed his mother but he could never make it in time. The fact that he could have to warned his mother against driving the car on that particular hapless night on several occasions before the accident remains a glaring omission. He could have called her on the phone, passed the message through young Clare or in fact warned her in person when he met her on the train three years before the accident or all of the above and anything else.
Before Henry's final time travel into the woods, he already knows that he is going to die by getting shot and being naked, having had no time to find cloths. As soon as he appears in the woods next to a deer, he should have known that a hunter might fire a shot in his direction. If he had simply ducked or moved behind a tree, he could have prevented his own death.
During Clare and Henry's fight about his vasectomy, Clare is seen working with a piece of handmade paper. She removes the mould and flips it upside down and presses on it to remove the moisture before couching it onto a piece of blotter paper. The camera zooms out and you can see it hasn't been flipped. Zoom in, zoom out again and its is back to being in the flipped position.
In the first scene that Henry appears naked on the floor after being shot, there is no blood left on the floor when he disappears. Or, at least the characters act as though there is no blood left. One might argue that the blood gets transported with the body when it time travels again; however, in the ending of the movie, the hunters find the blood-stained snow after Henry has traveled.
When Henry returns back to the time of his wedding he has gray hair. Upon his death he does not have gray hair, nor does he at any other "present time". While he might have gone gray and started coloring it at some point, it is unexplained how he returns with gray hair at his wedding (and on an earlier return to visit Clare).