In this video, the error saturates at around 190 but not close to zero. Does that mean it is stuck in local minima instead of global minima?
Local minima and Global minima
No this is not the case, because data contains some noise that means in linear regression dataset, all points are not on a single line, some of them are on the line, while others are close to the line. So The points which do not lie on this line will for sure contain error term equal to distance of the point from that line which is in this case you can say adds up to 190, and hence this is the global minima and not local one.
Hope this cleared your doubt.