Smoothbore muskets were considered reliably accurate at 80 yards. At that range, accuracy meant that a trained musketeer would reliably hit a stationary, man-sized target somewhere on the body. The depiction you've described, shooting through a window at 30 feet, is well within that range envelope and would not be a difficult shot even for someone without much training. 30 feet is very close range, and even a smoothbore pistol would likely have been able to make that shot.

A quote by George Hanger from 1814 is often used to illustrate the known qualities at the time:

A soldier's musket, if not exceedingly ill-bored (as many of them are) will strike the figure of a man at 80 yards, it may even at a hundred, but a soldier must be very unfortunate indeed who shall be wounded by a common musket fired at 150 yards, provided his antagonist aims at him

As /u/Lincolns_Ghost has alluded to, the problem with black powder firelocks was the black powder. Every shot left a thin residue called "fouling" that was slick and oily when hot (say, after firing a shot or three), but turned solid and chalky when cool. In either state, the fouling would build up after each shot, which effectively decreased the barrel aperture.

This is obviously a major problem, but there were ways of dealing with it. The first, and most widely adopted, was to use a ball that was undersized. For a British long or short land pattern musket (both of which were widely used during the War for Independence), that meant a true caliber of .75, firing a ball usually around .69 caliber. This prevents fouling from being a major problem until many shots were fired (apart from clogging the touch hole or other such obstruction) in terms of loading. But this also meant that the ball, when fired, would actually bounce or rattle down the barrel, causing small and unpredictable changes to its flight pattern that caused the erratic shot-placement that becomes more dramatic at longer ranges.

A second way of dealing with it - which was used in rifles before the minie ball - was using greased patches. Fit snugly around the bullet, it prevented the bouncing in the barrel by acting, more or less, as a sabot, smoothly pushing the ball out of the barrel with minimal erratic effects. This would come, however, at a dramatic cost in speed, and was one of the reasons that rifles were equipped by specialized forces, rather than the entire line.

The quote above and much of the information can be found in United States Firearms: the First Century, 1776-1875 by David Butler. I would recommend it if you're interested in the history and operation of firelocks of that period.

Smoothbore weapons are accurate up to 100 yards or so but were deadly up to several hundred yards. Past that you are still talking about major injury if you were somehow able to be hit.

In combat, muskets of the day were typically not fired until armies were within 50 yards or so of each other, and this is probably where the idea of their inaccuracy came from.

Rifles of the 18th century were accurate up to 300 yards or more.

The reason armies used muskets over rifles is a question of firing the weapon. Black powder is not an efficient propellent, and leaves a ton of residue in the barrel. After several shots with a rifle it is almost impossible to shove the bullet into the barrel without tremendous effort. It isn't until the invention of the minie ball that rifles become very viable, as the expansion of the minie ball cleans the barrel.

By contrast, smoothbore weapons the ball is a slightly smaller caliber than the barrel, meaning it is low effort to load and fire. 18th century warfare relied on massed fire, not necessarily accurate fire. It might take 30 seconds or more to load a rifle, but most people of the time could fire a musket 3 times a minute.

Sources: School of the Soldier, an NPS Manual. Also trained as a historic weapons demonstrator in the US NPS and a State Park Service.

There are other issues at play here, like bullet drop and a lack of sights on muskets, but this is the gist of it.

Regarding how accurate the average musket could be, you might be interested in this article detailing a series of experiments carried out at the Styrian Provincial Armoury in Graz, Austria: https://journals.lib.unb.ca/index.php/MCR/article/view/17669/22312

From a mechanical rest, the spread of the smoothbore flintlocks varied between 53cm and 118 cm at 100 meters. The author comes to a negative conclusion about the weapons' accuracy, but given that these were all "munitions grade" weapons and 200-300 years old the test seems to back up George Hanger's claim that a good musket could hit "the figure of a man" (presumably 45 cm wide) most of the time at 80-100 yards. At <50 meters the shot from a musket likely would have been pretty certain, and at 30 meters even their flintlock pistol was able to hit the target 99% of the time.

Targeting single individuals with a smoothbore was possible and did happen at times, however few soldiers actually achieved that kind of accuracy and even fewer could achieve it under combat conditions while listening to balls whistle past their head. In P. B. Hughes Firepower: Weapons Effectiveness On The Battlefield, 1630- 1750 he looks at a number of period "musket trials" which involved soldiers firing volleys at a target ~6 ft tall and ~100 ft wide and notes that the average soldier was able to hit it around 40-50% of the time at 100 yards. In combat, however, as smoke obscured the soldiers' vision and nervousness got the better of them, most resorted to loading and shooting as quickly as possible without any attempt to aim and accuracy dropped significantly. In reality the accuracy rate for a single volley at 100 yards seems to have never gone over 5% or so, and most battles from the period saw armies expend hundreds or thousands of musket bullets for every enemy casualty inflicted.

In short, muskets could be both fairly accurate and extremely inaccurate. It varied dramatically depending on the quality of the gun, the skill of the shooter, and the conditions it's being shot under.