A properly applied patch should resist inflating the tube up to 1.5-2 times the nominal diameter. This is useful for testing the quality of the patching work but also to find the tiniest holes that sometimes are harder to spot.
As other say, the definitive way to test is to inflate and submerge in water or to inflate and let overnight to see if it holds.
However: I you get these tiny punctures and specially if they develop on the inner side of the tube (or "high" on the face sides), then the problem may be a faulty or degraded tube. Tubes may suffer from chemical reactions which makes them prone to develop spontaneous pores. When such moment arrives it is best to buy a new tube (one that has not been in the shelves for too long).
Some other ways to spot a chemically damaged or degraded tube is that when inflating them outside the tire, they have irregular shape (thicker in one parts than other) or the valve spins towards the outside. Other may show cracked or rough spots (or other odd texture). Another symptom may be the tube looks "too black" (a normal tube is actually dark gray) and they feel sticky.