Easy! You just make sure that (a) historical events in any episode don't contradict historical events in other episodes, (b) the 'laws of physics' (however they have been set up in the fictional universe) don't change from episode to episode, and (c) people's personalities and the technological abilities of their equipment (for example what the TARDIS can do) don't change from episode to episode (unless there's an obvious rationale for the change).
I'd say continuity in show featuring time travel is basically no different from continuity in a show that doesn't. The only difference is that in a show that has time travel, you have the flexibility of characters going backwards and forwards in time and therefore being able to participate in events in a different order from their historical order - and, of course, events in different historical eras.
I don't like the TARDIS being so powerful. Not keen on the Master becoming Missy as a plot line.
I don't always like the stories being of a faster pace. Nor most of Murray Golds music, although I do realise he is talented and it's just the style I don't like vers the classic series music.
I do like many of the stories and I am pleased that at least three stories this season are 2 partners. Makes a refreshing change.
Whilst watching the new series I'm also watching season 3 of the old series. Back before the 23 November 2013 I started watching the pilot episode of The Unearthly Child. Then on the 23 November and once a week from then onwards I started watching the classic series in order.
Many episodes I've not seen so it was a good way to do it. I don't need to decide what to watch, the producers did it for me. As the seasons are so long I take the same breaks that existed 50 years ago between seasons.
If I was really nerdy I could watch then at precisely the same time they were broadcast as one Web Site lists the broadcast times down to the second!
http://www.drwhoguide.com/who_s.htm
I do try to make sure I see or hear every bit of the stories and if edits exist in surviving video, I try to hear the audio in the right position before restarting the video.
I'm watching them as partly intended. I. E. To be watched once a week and not all in one go or night after night. My TV is much larger of course and I'm aware some minor corrections were made to the film during the restoration process so it's never an exact reproduction.
Just seen Trap of Steel, episode 2 of Galaxy 4. It's not the greatest Who episode and that's unusual as most of the Hartnell episodes were fantastic. Great acting and good story lines.
The new series may at times be described as epic but in season 3 there was the one off episode, Mission to the Unknown. This featured no regular cast but did feature some Daleks and a few others, including the actor Nicholas Courtney. Following it was the historical 4 parter, The Myth Makers. That bared no relation to the Mission to the Unknown episode. However after it was the start of the 12 part story, Daleks Masterplan. Such a shame only 2 complete episodes exist. That truly was epic. I've heard every episode and this year and next, as it runs into next year, I intend to watch them, mostly via YouTube reconstructions people have put up.