M'yrnn is later shown to be suffering from the Martian form of dementia. For him to ask if everyone on Earth can fly is not a continuity issue, but an early sign of his mental demise.
As proof of who he says he is, J'onn shows M'rynn his favorite memory of them together. Since his father's presence that day was intended as a surprise, J'onn should have no recollection of M'rynn alone talking to his granddaughters, as he wasn't there to witness it.
When Supergirl goes to talk to M'yrnn when they are at his house, M'yrnn looks into Supergirl's mind and sees that she is Kryptonian - and therefore from Krypton. In contrast to this, at the end of the episode when Supergirl flies away from M'yrnn and J'onn, M'yrnn asks if all people on Earth can do this, implying that he thought she was from Earth.
When Supergirl punches a White Martian off his feet, you can clearly see her fist never even touches the alien.
During an argument, Maggie's father mentions the border wall being built to keep Mexicans out of the country. This is obviously a reference to the real-life presidency of Donald Trump, but within the show's continuity, his comment doesn't make sense: in "Resist", the penultimate episode of season two, it's revealed that President Olivia Marsdin is literally an alien from outer space, and earlier in the season in "Welcome to Earth", she signed an executive order offering aliens such as herself full citizenship if they so desired it. If she's that tolerant of extraterrestrials, it seems unlikely that she'd be so intolerant of legal aliens as to resort to such an extreme action in foreign policy like building a wall on the border.