Keep your stitches small and snug throughout your circuit. An embroidery hoop comes in handy to keep the fabric flat.
Keep power and ground lines far apart from each other. A short between power and ground will prevent your project from working and may even cause your battery to heat up.
Use a multimeter's continuity tester to check your circuit for shorts. The meter will beep any time the two probes are electrically connected.
Put one probe on power and one probe on ground. There should be no beep!
Check your circuit for shorts after finishing each path in your circuit. This way if you do discover a problem, you will know the likely location of the stray thread/short circuit.