I think it's a mix of several things, which is what makes it so hard to define. One of them, as emile says, is that
continue implies a reference point, whereas
last implies a period in its entirety.
Taking
last first
, I might say either of the following :
The festival lasts for three days
The festival starts on Monday and lasts until Wednesday.
The starting point may be implied by the context but is always there - so in
the film lasts for three hours, the implication is "from the time it begins". And it's the same for the end point - we know the whole period.
Last then takes us from start to finish and emphasises a continuous period of time for an event.
On the other hand, I could say :
The film continued after the interval. Here we know the starting point but don't know the end point - this suggests that
continue is more involved with an action than a period or an event.
When I put
continue into a concordancer, the majority of the examples that came up were continue + infinitive : eg
they continued to argue that ... This again suggests that
continue expresses an action rather than an event - which may explain the "oddness" of
The movie continues for three hours where "the movie" is seen as an event, and the emphasis sems to be on the period of time.
But if we change it to
The movie started at 8 and continued for three hours without a break or
It's a really long film. The first half lasts two hours and then after the interval it continues for another hour and a half - suddenly it sounds a bit better. It seems there's an implied action (which we would never actually express but which might have a meaning something like
to be shown, or
to play) in there after
continue, and the emphasis is on that, rather than on the period itself.
It seems to me that it's a mixture of :
a) emile's explanation -
continue must have an reference point, which may be either the start or a restart after an interruption.
Last on the other hand doesn't need one. I can tell you
The film lasts for three hours without knowing exactly when it starts or finishes.
b) the difference between placing the emphasis on a period (
last) where if we specify the start we must also specify the end point or an action (
continue) where only the start (or restart) points are necessary. So I can say
The festival continues from Monday but not
*The festival lasts from Monday.
c) Breadbaker's point that
continue is sounds odd in what is probably a conversational context :
The film goes on for three hours does seem more feasible. I don't think this is a major factor, because I'd argue that continue is neutral in style rather than forma, and therefore should be OK in conversational contexts. But it's true that
goes on is less formal, and this probably adds to more comfortable feel of the sentence.
If this seems a bit muddled, it's because it seems to me these three things are all mixed up in each example. As I say, it's a combination of the factors rather than just one thing. But if I had to plump for just one, I think I'd go for the period vs action explanation.
Tricky one ....