The 'th' pronunciation typically isn't pronounced by people because most Singaporeans are lazy speakers! :bsmilie: If pronounced correctly, your tongue will actually slide back between your teeth. Try sticking the tip of your tongue between your teeth and withdrawing it sharply when saying three, it should fix your problem.
The other big problem amongst Singaporeans is always the fricatives like in fries, which often turns into flies.
Ironically, this is what makes up the Singaporean accent, poor pronunciation.
If you actually wind up pronouncing things clearly, people sometimes mistake it for a foreign accent, because it doesn't sound local.