Why can't I tap Pokémon on the map?

As of v0.29.0, this is a known bug. Objects on the map will become unresponsive to taps.

The best bet here is to simply close the app (i.e. shut it down, don't just minimize it), and restart the game.

Additional info: This bug is known to occur more frequently after making use of the "battery saver" where by the screen goes dark when the device is held upside-down. Waking up the screen again will often cause this bug.

0.29.2 update - The bug still exists, but seems rarer. Due to high server load, you will simply not receive data from it, and the game will lag, or stop working.