Aside from any two parters, are the Dr. Who episodes intended to represent a consistent beginning-to-end timeline for The Doctor, or do they bounce around willy nilly, or rather, timey whimey?
Yes, in general, the shows are intended to follow The Doctor's own personal timeline. In addition, the show tends to follow a chronological progression of the companion(s) lifetime, at least while they are with The Doctor. In general, The Doctor does not bounce around back and forth within a companion's life.
There have been a few exceptions to those two rules, though they're clearly called out when they happen:
- Father's Day: The Doctor and Rose traveled back along Rose's personal timeline, causing bad things to happen.
- The Big Bang: The Doctor traveled into Amy Pond's past (as did Rory and Amy, technically, though they took the really long way).
- The Impossible Astronaut: The Doctor that was present in the beginning of the episode was from hundreds of years later in his own timeline than The Doctor that appeared in act II. (Specifically, the initial Doctor was from the same point as in future episode The Wedding of River Song).
- Any of the The XXX Doctors; The Day of The Doctor: Obviously, any episode that includes more than one Doctor on-screen at a time will be a violation of this rule, if nothing else than for practical reasons: the "future" Doctor would not have been cast yet at the point in the "past" Doctor's timelines where that episode occurs, so we must be seeing it from the timeline perspective of the most recent Doctor in the episode.
Note that River Song is the huge huge exception to this rule: for most of her tenure as a recurring character, River's past experiences were always The Doctor's future, working roughly backwards. The two of them met, technically in The Impossible Astronaut, but more "officially" in Let's Kill Hitler; from there things seemed to progress roughly forward for the two of them, but in a much more haphazard way.
Also, while we are meant to assume that the adventures with The Doctor and Clara are both progressing in the same direction, there was at least one throwaway line of dialog that went like this:
Clara: See you next Wednesday
The Doctor: Well, a Wednesday
However, we haven't seen any indication that he might travel back to a previous Wednesday and retrieve her; she generally remembers everything that happened in previous episodes and does not ever mention things that will happen in future episodes.
It's a show about time travel. They visited the formation of the universe in the first Doctor story The Edge of Destruction and the Tenth Doctor story New Earth is set at some huge number of years into the future (beyond the destruction of Earth) as is the First Doctor story The Ark - so no, I don't think they're in any kind of externally consistent chronological order. or yes, but time isn't a strictly linear progression of events.
There was a theory in season 7 that the Doctors timeline was in reverse to the episodes (while Amy + Rory were forward). This is based on props from later episodes showing up in another.
Also some of the Doctors dialogue in earlier episodes makes more sense if you realise that the doctor knows the outcome of his travelling companions.
There is another theory that because his companions become locked in time when he meets them, that he knows that his companions are immortal until a certain time/location (like the Doctor going to Trenzalore)
It also appears to be hinted at in Season 8. Episode 2 the doctor does the following:
After realising the Doctor has to heal the Darlek, he instead time travels back to England to pick up a school teacher, and tells her to solve the situation (but doesn't know how she should do it). It is possible the Doctor is aware when Clara will die, so in doing this he knew that she could not be stopped in recovering the Darleks memory.