Optimizing product tests?
My thoughts about high volume testing:


Minimize operator interaction with the test object. Preferably place a number of test objects in a test bed, push a button, wait for OK/FAIL then remove the faulty test objects for investigation at another station. Never keep the line halted because of a faulty test object.
If the operator needs to put in serial numbers or other manual entries, use pre-defined barcodes with a scanner if possible. This will minimize the human errors.
Bed of nails are fine in high volume production tests. At lest if your PCB is reasonably sized for a multi PCB fixture. One great advantage of test points compared to a test connector is that you don't need to route sensitive signals all over the board. On the other hand, sometimes you can't do without a connector because of board space or signal integrity issues. 
If you need to have connectors attached somewhere to the test object, make sure that the ones on the test equipment are on adapter boards or with cables that can be easily replaced as they wear out. You might even need a counter in the test software to keep track of usage and maintenance schedule.
Make thorough analysis of how much time each test step takes, try to find steps that can be done in parallel. As an example,you might find that programming a firmware takes a long time but the analog and digital measurements are done fast. Then you might want to make a large parallel programming test station but use low capacity station for the measurents. That way you will free up expensive measurement equipment and keep the flow going even if a few units fail at programming.
Make use of automated vision inspection systems to catch the first errors coming out of the manufacturing. Time spent on testing a PCB that was missing a resistor is waste...
Setup a database for handling the output of the test equipment. It is much more convenient to analyse a large amount of test data from a database than from a pile of text files.
On PCB's with lots of advanced digital components you might want to consider boundary scan testing. Unfortunately the price for equipment and software for performing boundary scan tests can be high. You have to weigh it compared to having products failing in the field.