Must say that this is beyond what one would expect for a cutting, so nais.
Question: I know that the leaves will continue to brown and die as it adjusts to the new environment (so I don't think I should be worried at its current state), is it better to remove the browning leaves or should I let them die in place?
Thx.
Unheimlich**

Just make sure that

1) The cutting is in a place with decent airflow
2) The soil is not too packed, nor too wet

then you can rule out any root rot, which is as far as I know the only reason why you should be concerned with browning leaves.

I have adapted salvia plants to a low ambient humidity (around 25-30%) and yes the leaves do brown in the edges and become more curly and sturdy, but as long as there's green in the leaves, they are doing their thing - so I wouldn't cut them unless you are in a rush for harvesting.

Eventually, the new pairs of leaves will show less brown. Mist the plant a few times a day during the adaptation process if the leaves deteriorate too fast or too much.

Vodsel, thx. They have been browning just at the sides (with curling) or at the tips. Not so much as to make the leaf seem to be dead, so I will let it chill. Wasn't desperate to harvest it, it was more of "I would hate for these leaves to go to waste."
The soil seems good, I went with Gibran2's famous Miracle Grow Moisture Control, with a 1/4" layer of perlite at the very bottom just to ensure no stagnant water gets hung up in the pot. Then I watered a tad bit the first day, followed by a full watering the second day, will now wait for soil to dry before next watering.
Misted twice the first day, but trying to keep from misting, as it seems to be the death of many plants from what I understand.
One last question... would a ceiling fan for airflow hurt the plant at all? The leaves shake a little in the moving air, but less than what a very light summer breeze would do.

I can relate to the "I would hate for these leaves to go to waste"... problem is, by cutting leaves that still are working you take resources away from the plant, and if you have the long term idea of having a couple plants that are used to your place and give a steady harvest, these leaves will pay off more now in the plant than drying in a plate. Even if partially dry and curly, they are synthesizing valuable carbs for the plant. Once the mass of leaves is large enough, you can start harvesting the larger, drier leaves and take new cuttings.

I haven't tried yet, though, using partially brown-dry leaves. I guess that the fact the leaves have dried in the plant, or once harvested, should not affect salvinorin content much. Can anyone report about it?

And about the ceiling fan, gentle airflow is good. Just keep in mind that it will make the humidity in the soil and the leaves evaporate faster, so it requires checking on it and watering a little more frequently.

The photos show a very healthy plant. Slight browning doesn't mean the plant is sick or that the affected leaf is dying. I'd just leave the plant alone and let it grow!

if you can I would grow it outdoors for the summer..they grow much faster outdoors than they ever will indoors as long as the temperature is not like freezing. Most place would be fine for the summer as long as you keep in in filtered light and dont let it dry out.

That's a nice looking cutting. I still haven't bought mine. PM me and tell me where you got it if you would. Thanks.