There's probably a few contributing factors. Here's my best guess:
Lin is taking more outside shots, and that's not what he's best at. Last year, he mostly worked inside so his FG% was higher, and he was more of a threat to create shots for others. Here's a shot chart from http://basketballreferenc
Airballs are typically the result of a lack of strength. That's why you see it more at the end of games than at the beginning. Good shooters will tell you that they don't mind missing the occasional shot, as long as it goes long. That's because they're looking for an indicator that they still have their legs. If they start missing short, it means they're fatigued and will shoot poorly going forward despite accuracy. Jeremy Lin's airball against the Heat came at the end of a game where he played 34 minutes and was at times responsible for guarding Mario Chalmers (4pts on 1-5 shooting) and Norris Cole (2pts on 1-4 shooting). His last shot before that was a missed 10ft gimme in the paint, possibly also an indicator he just didn't have his legs. That was the first shot he had taken in 12 minutes of game time.
He's still recovering from MCL surgery. Does he have his speed and cutting ability back yet? Probably not all the way. It's been about six months since the surgery, and its likely he's still rebuilding the strength in his leg. That would affect his shot, his ability to contribute a lot of minutes, and his ability to do the kinds of things he's good at, like cutting to the lane, that will force defenders to give him more room on his shot.
He's in a new system, again. At least when he was playing in NY, he had two months to hang out with those guys and practice a bunch. It's probably one of the reasons he played better with the bench than with the starters. In Houston, everything that mattered changed when they got Harden two days before opening night. Harden is a lot like Lin, only better in every way with some facets of his game that Lin just doesn't have. It's going to take him a minute to feel comfortable playing next to Harden, and until he does you're going to see the occasional ugly shot/pass/possession. To a lesser extent, this is also true with Omer Asik and the library of Rockets forwards. As you can see from that shot chart, Lin's favorite play was running to the basket on the right side. You could imagine that some amount of spacing and decoy work from the other players would make that a lot more effective, and that's something he and his new teammates are going to have to work on. Until that happens, I wouldn't be surprised by the occasional really ugly play.
For what it's worth, he's averaging a full assist more than he did with NY and a full turnover less on a team with less front court offense and three point shooting. I consider this the most important change since NY. If he'd regressed in this part of his game, it would be hard to argue that he'd deserve his starting minutes by the end of the season. Regardless of his points per game, his assist/turnover ratio is likely the one that Rockets are focused on and happy about.