There is strong evidence that shows that increased concentrations of the mass of particulate matter below 2.5 in microns (PM2.5) leads to adverse health effects in the general population. Exactly how aerosols cause health problems is not well understood and is a active area of research. So far it appears that carbonaceous aerosol, both organic and black carbon, are the bad actors. The primary health impacts appear to be heart attacks and compromised lung function.
The most famous historical example of the health impacts of smog is the “Great Smog” that covered London for 5 days in 1952. It was particularly cold, leading to city coal fireplaces working overtime. In addition, a high-pressure system made the atmosphere stagnant with no wind. People were unable to see but a few feet. Traffic was halted. The air had a rotten-egg smell that is a signature of sulfur emissions. It is estimated that the event lead to the deaths of up to 12,000 people. A similar event occurred in Denora, Pennsylvania in 1948. Some cities in China are beginning to see larger PM2.5 concentrations.
The primary indication of a bad smog day is the fact that you can’t see as far through the atmosphere. This reduced visibility is caused by scattering and absorption of light between you and what you are trying to see. This same thing happens between the sun and the surface of the planet. Larger PM concentrations in the atmosphere reduce the amount of light that reaches the surface, which can lead to different effects on the climate. More light scattered back out to space leads to a overall cooling of climate. The absorption of light by some aerosols (black carbon, in particular) leads to a warming. There are other more complicated processes that can lead to changes in how and when clouds form or how often they rain.
Aerosol formed from sulfur dioxide emissions (an important component of coal combustion) lead to acid rain, making lakes and streams more acidic. The particles also deposit onto surfaces, eroding them over time. With emissions control, this is not as big a problem as it used to be, but this process affected a lot of buildings. This is a sandstone figure over the portal of a castle in Westphalia, Germany, photographed in 1908 and again in 1968. The figure has been rendered almost unrecognizable.
Here are some EPA resources related to air quality.