Don't forget NO DRUGS....Death penalty for anything over 15g.
L-1011...funny that you mentioned chewing gum and the trains in the same post. This is the reason that gum was 'banned', as at the MRT stations there is a door at the edge of the platform that opens and then the train door opens. People were sticking gum in these doors and getting them jammed. Although, you are still allowed to bring 'small' amounts of gum into Singapore.
Also remember, that you cannot take duty-free cigarettes in either. Duty has to be paid, although, if you are honest enough in declaring that you have a carton or two, the customs officers have always let me thru with no excise payable.
People are also told to stay away from the Istana Negara at night time (apparently you will be taken away for questioning for a legal excuse for being around there), although I had no problem, and even got into a conversation with a couple of the armed guards at the front gate.
Overall, while I would not say that Singapore has strict laws (no stricter than anywhere else), it really is one city in which one can feel absolutely safe in walking the streets at night and the people just love us Aussies.....could live there if they would give me residency