Adjustable Voltage Regulator behaving weirdly
Page 17 of the datasheet specifies that the regulator you are using requires at least 100m&ohm; of output capacitor ESR for stability -- I suspect the control loop is out of whack because the output capacitor ESR is too low.  Try sticking a resistor of anywhere between 1&ohm; and 10&ohm; in series with the output cap and seeing if that fixes it -- if it does, that indicates the capacitor's the problem.  (Note that modern tantalum and polymer electrolytics can have ESR values that are too low to stabilize an older LDO like yours, so it's not purely a ceramic cap problem.)

Of course, you could also try switching to a more modern regulator that doesn't have such annoying requirements on output capacitor ESR.