November through April is the best time to visit San Blas. The weather is dry, the sea is calm and clear, and the no-see-um gnats (jejenes) that plague the town in summer are at their least ferocious — though they are never entirely absent, so bring insect repellent regardless. This is also when the northwest swells arrive for surfing.
May through October is the rainy season. The humidity is oppressive, the gnats are at their worst, and the mangroves flood. Birding is actually good in some wet-season months when migrant species pass through, but the general experience of being in San Blas is considerably less pleasant. The town largely shuts down for serious tourism in the depths of the wet season.