[Continuity Errors?]
0) Regeneration accent theory (not a fact, but still it was asked at a comic con and the writer said yes) there has been a pattern in new who where when the Doctor regenerates there accent changes to match the companion as to make them feel more comfortable. E.g. 9 was thinking of Rose so his northern accent changed to a standard/London one, 10 was not in the precedence anyone so again a standard accent, 11 was thinking of Amy so accent change to Scottish, however 12 should have regenerated with no accent and Jodie clearly has Yorkshire one.
1) "Half an hour ago i was a white haired Scotsman". In twice upon a time she was in the TARDIS for 1 minuet post regeneration until she began to fall, she was high enough that you could make out one large city and a few small towns at night (which is not that high - airline height if that).....and claims to be falling for approximately 29 minuets (unless Rule 1 - the doctor lies still stands) and fell at such a velocity to shred the upper aluminium shell of a train only (i don't know how much force that would be but using F=ma, where here approximate weight is 50 kg we could find the acceleration and use that to calculate height eventually)
Now the current world record free dive was the Red Bull upper atmosphere jump. On 14 October 2012, Baumgartner flew approximately 39 km and that jump took 10 minuets....so there is some time missing here. Which is why i think "The women who fell to earth" only refers to Grace and not the Doctor.
2) "Don't be daft there's no such thing as aliens" First contact with previous continuity was the Slathine and big ben in 2006 (we know the episode does not take place before 2006 because of the phones in the episode). Since the lost earth humans all over the world know the existence on aliens. Yes this could have been cancelled when the 11th reset the universe but the cube invasion was considered alien - so again people in the DW universe should know of aliens being real.
3) "Same software different case" as we know from the 50th the all the sonic screwdrivers are connected to each other (because even though they have been destroyed and dis guarded in the past, the TARDIS gifts it to the doctor), so since she build this one is it still connected?
4) "Been a long time since i bought women's clothes" As we know (regardless of what Missy says) the Doctor has always been male except now. Timelords tend to stay the same gender (as seen with the general). But the TARDIS has a wardrobe with female clothes in it so maybe thatch what she meant. However on the (sensitive) topic of clothes, she did a lot of running this episode in 12th clothes, if i understand correctly girls find running hurtful without a bra, so how did she not comment on that (when according to google search JW has 34B size breast) unless girls of this size do not find running uncomfortable.
5) The TARDIS. As we know from voyage of the dammed and 11th hour, in a crisis the TARDIS lands on the nearest largest point of gravity i.e. the earth, also from 9 and 10 we know the TARDIS can be called with the key or a CD. SO how can the TARDIS materialise on a different planet when it was defiantly crashing and should have felled to earth.