There are many limits in machine learning that can be listed.
Of course a principal machine learning limit lays in the data used to train the machine learning algorithms .
If the data are good -and with data I mean if the context to recognize is modelled correctly- then the machine learning results that derives are good.
A famous example showing machine learning limits is the one given by the Apple Newton tablet for hand writing recognition. In one of “the Simpsons” episode they make jokes about Newton tablet for its error in recognizing “Beat up Martin” as “Eat up Martha”