In one scene where Florentino is sending a telegraph he is also writing. So which is he doing, sending or receiving! To compound this, he is writing with his left hand, but in the rest of the movie he writes with his right hand.
When the Widow Nazaret takes refuge in the Ariza home and has a drink with Florentino's mother, the mother reaches over as if to replace the cork in the decanter but doesn't do so; in the following reverse shot, the cork is in the decanter, but upon cutting back to the original angle it is again out.
In the beginning when Florentino Ariza is lying with America and the Church bell rings, she says 'Its Pentecost' and then she puts her hand over his body. The same scene is repeated towards the end of the film and is shown from a different camera angle, but here America first puts her hand over Florentino and then says 'Its Pentecost' (not before).
The trip that Florentino Ariza takes upriver where he experiences his first 'tryst', prominently features a zipper being (un)zipped. Since the zipper was not invented until 1913, nor patented until 1916, this would have been some feat.
The wedding of Dr. Juvenal Urbino and Fermina is a Modern Catholic Mass. Actually, during the late 19th century and the first decades of the 20th century a Traditional Latin Mass would had been conducted instead.
When Dr. Juvenal Urbino visits Florentino Ariza he asks him
what kind of music Ariza likes. "The music of Carlos Gardel", Ariza answers. The time of the action is somewhere between 1890 and 1895. Gardel was born between (the date is not confirmed) 1883 and 1897. So, he was just a kid at that time, and he couldn't be known at all as the famous singer that died in a plane crash in Medellin (Colombia) in 1935, at the age of 48 or 52.
A man utters a New Year's speech in which he emphasizes the year 1900 being the beginning of the 20th century. In fact centuries are counted from the year 1 to the full hundred, which makes 1900 the last year of the 19th century. Analogical error was very common in the media in the year 2000.