Correct Him – or Let It Go? When Should Mistakes in Shul Be Corrected?

When should a ba’al tefillah or ba’al keriyah be corrected – and when is it better to let the mistake go?
If someone’s talking, pacing, or other behavior is distracting the congregation, when is it appropriate for a gabbai or rav to intervene?
What about a chazzan who is davening too slowly? When should he be asked to speed up – and when should the tzibbur simply be more patient?
Which shul halachos should be enforced, and which are we too strict about?