Oh yes there are some good spotting locations inside the transit area at Changi.
If you are transiting in the morning, go to the Cactus Garden. It's at the left side of Terminal 1. You should have a good view of movements.
On the way there, the former McDonalds area offers a commanding view of the Central Apron.
The glass in the transit facing north into the central apron has a very dark tint, so for this part the public area is better.
Hope that your aircraft's assigned gate is on the western side of the airfield.....with that you will be able to take photos of the movements on Runway 20R/02L.
If you transit is in the afternoon, it is more interesting. Go either to the Sunflower roottop for a good view. You should be able to take some nice pictures of aircraft on climbout. The T2 apron transit, which has lots of little eateries, offer a great viewing area of aircraft movement and the glass is very lightly tinted. Lots of SQ and MAS traffic there and runway action too.
You can move between the terminals either by foot or the Skytrain. Hope that helps.
I would like to hask for suggestion that where I can spot during my transit in SIN on my way to KUL and back HKG?
Was someone looking for a KLM triple......