Somebody who talks during the chazarat haShatz, especially about secular matters, endangers the whole shul (Mishna Berura 124:27). If he disturbs otherpeople’s davening (and this goes for anything that is distracting, such as wild shuckling) is over on gezel tefilla. This is much worse than robbing someone of money as it is impossible to return the gezel.
Someone who does not wear a hat and jacket in a shul where EVERYONE does so is maybe (today people know that there are different modes of dress) acting improperly on his own private cheshbon (today many people do not wear hats or even jackets on weekdays, even in Chareidi communities – it usually depends on the type of work they do).