It's not a mistake, and conventional current is not wrong or backwards.
The labeling of one polarity of charge as "positive" and the other as "negative" is totally arbitrary. It could be done either way and everything would still work out the same. Franklin didn't choose wrong; he just chose. Labeling protons as negative charge and electrons as positive charge wouldn't change anything.
Electric current is a flow of electric charge. Charge can be positive or negative, and both types of charge can flow in electric circuits:
- In metal wires and carbon resistors, electric current exists as a flow of electrons.
- In batteries, electrolytic capacitors, and neon lamps, current exists as a flow of ions, either positive or negative or both (flowing in opposite directions)
- In hydrogen fuel cells and water ice, current exists as a flow of protons.
- In semiconductors, current exists as a flow of holes, which are not quite the same as an absence of electrons.
(The Hall Effect can be used to show whether a charge carrier is positively charged and flowing in one direction, or negatively charged and flowing in the other.)
If you considered only the electron flow as current, your calculations would be wrong. You need to consider the net flow of charge, no matter what the charge carriers. Conventional current abstracts away the different charge carriers and represents all of these different flows as a net flow of positive charge, simplifying circuit analysis.
Conventional current is not the opposite of electron current. Electron current is a subset of conventional current.
In other media, any stream of charged objects may constitute an electric current. To provide a definition of current that is independent of the type of charge carriers flowing, conventional current is defined to flow in the same direction as positive charges.