You raise many interesting point, NeitherExtreme.
How much of an established theory needs to be falsified before the whole theory is abandoned? There is no simple answer to this. In practice what happens is that someone comes along with a theory (eg Newton's theory of gravity)which appears to answer key questions of the day, is open to the possibility of falsification through observation and experiment but is in fact confirmed by these observations. However, because no theory ever contains the whole truth, as time goes by instances gradually emerge in which the predictions of the theory are not supported by observation (ie the predictions are falsified). A trickle at first, these instances become increasingly more common. At this point a new theory is produced which explains the observations that are contrary to the previous idea. (eg Einstein's replacement of Newtonian gravity by the general theory of relativity.) An important point is that the old theory is not simply "junked". Newtonian physics remains good enough to predict the outcome of many processes to this day. Only under certain specialised conditions (eg approaching the speed of light) are the limitations of Newton's theory encountered and the more sophisticated Einstinean approach needed.
Does scientific theory do no more than "join up the dots?" There is a great deal of truth in this suggestion. Any theory, any claim to knowledge contains elements of the imaginative. The point is that a scientific theory, as opposed to more speculative philosophy, is required to join up the dots in a way which exposes the theory to testing by observation and is therefore open to falsification. Anyone with an imagination can join the dots. The challenge is the do so with an account which is not only open to falsification itself but actually survives the empirical tests which the scientific community subjects it to.
But at the end of the day, every theory is limited and fallible and in time its limitations are bound to be exposed by the very process of falsification through observation.