In my brief set of lost thoughts, most of which were wrong, I referenced Jacks magically growing beard from the episode “The Beginning of the End”. In this scene, Jack and Hurley play basketball and chat. At one point, Jack mentions that he’s thinking of growing a beard, at which point he misses his shot with a thud. In each subsequent shot of Jack, his beard is growing longer and darker. Near the last shot, he has actual whiskers as opposed to just a shadow on his face. The original video is linked below :

I’ve also grabbed some screenshots of the scene which you can see below :

0:16 Jack Greets Hurley Clean Shaven

0:36 Jack misses shot, says ‘H’

0:48 Thinking about growing a beard (Misses shot, big thud)

0:57 You’d look weird with a beard dude, that’s H-O

1:04 What are you really doing here jack?

1:11 Just checking on you (in the same shot as the previous image)

1:17 Jack listens to Hurley accuse jack of seeing if her was going to tell

1:26 You’re up

2:08 Water under the bridge.

2:11 I don’t think we did the right thing

2:15 Jack brushes off Hurley

2:18 We’re never going back

Going back to the first :

0:16 Back to the first shot for comparison

Now, comparing the first and last shots, it’s pretty evident that Jack grew a beard from the start to finish of this scene, and it started when he talked about growing his beard.The question is whether it was intentional, or whether it was just a continuity error. There are a couple of reasons I find it difficult to believe that it is continuity.

The beard grows sequentially in the order it is seen in separate shots, typically continuity involves objects moving for example from one hand to another and then back again as new shots are interleaved with shots from a different day. It is not impossible, but it would be a coincidence that the beard was growing in the order it was shot. Unless they filmed the scene sequentially throughout the day and Jacks beard continued to grow. The final shot shows sun light streaming through the window in the same direction and shape as it did when Jack entered (not shown in this clip). This could be explained by using common sense and filming the wide shots of Jack entering and leaving together so the sunlight would be in the same place.
On the other hand, I am sure actors have their make up touched up between shots and it would be pretty hard not to notice Mathew Fox was getting a little bristly.
Assuming that this is intentional, what could it mean? One simple explanation is the passage of time. While they played some basketball, time passed at a much faster rate causing Jack to start growing his beard. Who knows how or why, but this is lost. Hurley conveniently already has his beard, or whatever it is that lives under his chin, so the same effect could not be seen, although interestingly enough, there doesn’t appear to be any continuity issues with his beard, or anywhere else in the scene.
Another wild (and off the wall) possibility, and this is not backed by anything other than a beard that grows quickly, is that maybe this isn’t the real Jack. I hesitate to claim it is smokey since smokey hasn’t been seen off-island, and always seems to be the first idea that people leap to when something odd happens off-island, but if something was channeling Jack, and it got the idea of growing a beard, it might start to manifest one as part of it’s appearance. It could be some weird part of the story that we haven’t seen yet, like Jack died in the 815 crash but lives on because the aliens will it or whatever.

Credit for spotting this has to go to Mrs. Gibson who actually spotted it when we watched it, which is the main reason I can never get away with anything. The eyes are always watching. Always.