Singapore's reputation for harsh laws is not undeserved: don't expect any special treatment for being a foreigner. Despite the surprisingly low-key police presence on the street, they appear pretty fast when something happens. Police have broad powers and you would be unwise to refuse any requests they make of you. If you are arrested, you will be entitled to legal counsel and contact with your embassy.
Don't even think about importing or exporting drugs. At best, you'll get a long jail term; at worst, you'll get the death penalty.
Serious issues with retailers are unlikely (the worst you'll probably get is lethargic service), but if you've been ripped off or taken for a ride, contact the Small Claims Tribunal. Tourist complaints are usually heard within two or three days.