So I've noticed that the saddle on my Yamaha FG730S has started leaning towards the headstock.

Just now, I've come back from my local music store, and the guitar tech there said it was okay, and it was just because of weather fluctuations. I don't feel completely reassured that he is right, so I'm asking all of you:

Is a leaning saddle anything to worry about?

Oh, as for the leaning, it's.. I would say, maybe about 5-10 degrees off from standing straight up.
More than likely that's normal. The pull of the strings as they go across the saddle will be in that direction and down, so it's normal for the saddle piece to want to lean toward the headstock a bit. If it's excessive however, then you'll lose tone and sustain due to the fact that the bottom of the saddle isn't resting flush against the bottom of the pocket for it in the bridge. Just keep an eye on it to make sure that the bridge isn't cracked allowing the saddle to lean farther than it should. This will be really evident as there would be obvious cracks on one(or each) side of the bridge. Then you'll have problems.