It's a good question, because the history of the use of gestures is notoriously difficult to pin down, since so much of the history went undocumented. As Keith Thomas writes in the introduction to the book A Cultural History of Gesture, "Nowadays the study of gesture is primarily the business of anthropologists, linguists, and social psychologists" in part because "historians cannot observe the bodies of the past in motion". Nevertheless, even though there is oftentimes no direct evidence, "the sources from which inferences [about gesture] can be made are surprisingly rich."

Unfortunately, that book doesn't deal with the subject at hand (pun intended). Probably the most scholarly source on the use of the middle finger as an insulting gesture is the article "Digitus Impudicus: The Middle Finger and the Law" by Ira P. Robbins, published in the UC Davis Law Review in 2007. According to Robbins, there is evidence of the middle finger being used in ancient times as an offensive gesture in Greece and Rome, though it doesn't necessarily follow that it has been in continuous use since then. Gestures go in and out of style, and there are plenty of cultures, even in Europe, where the middle finger did not necessarily have an offensive meaning until the spread of American culture much later.

As to the gesture's offensiveness in the United States, Robbins cites the book The Finger: The Comprehensive Guide to Flipping Off by M.J. Loheed, et. al, to claim the use of the gesture probably goes back in American culture to at least the late 19th century. In 1886, the baseball pitcher Charles "Old Hoss" Radbourn snuck in a middle finger in a team photo of the Boston Beaneaters. That might be chalked up to coincidence, or even mistaking a cigar for a middle finger, except that Old Hoss did the same thing in an 1887 photo used for a baseball card issued by Old Judge Cigarettes.

The written evidence is a little more ambiguous. According to Green's Dictionary of Slang, the first use of "the finger" comes from the January 19, 1876, edition of the St. Louis Globe-Democrat newspaper, which wrote:

"He is told by his equally ‘busted’ companions to ‘stand him up,’ [i.e. a bartender] ‘give him the slip,’ ‘put up your educated forefinger at him’."

According to the Oxford English Dictionary, the "forefinger" means the index finger. However, "educated forefinger" seems to be a euphemism here for the middle finger ("educated" because it's graduated to the higher position).

Another early instance Green's finds is in the Standard Dictionary of 1893, which gave under the headword "finger" a definition for the phrase "to give one the f[inger]":

"To give one the f., To disappoint one after holding out hopes that his desires would be fulfilled, turn a cold shoulder to one."

Another early visual instance sometimes pointed to is in the 1928 silent film Speedy starring Harold Lloyd. In it, Lloyd ever so briefly flashes a middle finger at himself while looking in a fun-house mirror.

But the more direct acknowledgement of the middle finger with a meaning as an offensive gesture didn't really appear in print until the 1950s and after, when media became more permissive. The earliest instance the Oxford English Dictionary cites comes from the November 19, 1957, edition of the Pasadena Star News:

"He was going home, off duty, in his car late the other night, and a car full of young punks drove up beside him. They gave him the finger, and then held up a knife."

Even more unmistakably, Green's cites the 1963 book City of Night by John Rechy, which contains:

"...the cop, searching records to find a suspect who fits my description, says I gave him a fuck-you finger..."

And:

"With the cigarette holder clenched between her second and fourth fingers—the third finger, erect, supporting the holder—she aimed an unequivocal fuck-you symbol at the world Outside..."

Around the same time, "flip the bird" first appeared in print, according to Green's. The first known instance comes from the August 19, 1959, edition of the college newspaper the Daily Tar Heel:

"She was playing bongos in the paddy wagon and flipped the bird to the chopper before she lost her head."

Without having seen The Inspector General, I can't comment on it directly. The OED does say that there were other uses for "the finger" around the same time, though they seem to be related. They date the meaning "to get the better of (a person); to deceive, to cheat; to take advantage of" to 1874, though they call it "obsolete", with the last instance being in 1892. The meaning "to reject, dismiss, or get rid of (a person); to give a person the ‘brush off’" dates at least to 1889, and the OED gives the last instance of this usage to 1949, but calls it "now rare". Green's, however, seems to take the position that this usage may have always been a euphemism for the obscene meaning, so when the 1893 Standard Dictionary wrote that it meant "to give the cold shoulder", it's really saying it meant, "to tell someone fuck you".

So what was the intention of the 1949 film? It was very likely a joke, the filmmakers giving a nod to the audience that they were going to do something dirty but then didn't. There is evidence the gesture was already in some common use by then. The filmmakers likely knew the gesture and knew their audience would understand it as a joke about that impolite gesture. But with issues like this, it's always difficult to say with complete certainty what the intent was, unless the cast or filmmakers addressed it directly at some later point, which seems doubtful that they did.