The late Bob Pease, in his book "Troubleshooting Analog Circuits" (a truly excellent read BTW) had some wise words regarding the output capacitors on 3-terminal voltage regulators on pages 135 and 136:
"But in all cases, on all the parts [3-terminal regulators] I know, an electrolytic capacitor will work, and a film or ceramic capacitor won't work-its series resistance is just too small. Now, if you put a 1 Ω resistor in series with a 1 µF ceramic capacitor, the filtering will probably be adequate around room temperature; the loss factor is then similar to a tantalum capacitor. But if you take it to -40 or +100 °C, the ceramic capacitor's value will shrink badly (refer to Chapter 4 on capacitors) and the regulator will be unhappy again. It may start oscillating, or it might just start ringing really badly."
Remember, this was back in the day when ordinary electrolytic caps has ESRs of an ohm or so - not the low ESR parts currently common in switching regulators. Also realize that the output capacitor is the loop compensation for the feedback/gain in the regulator. Technically, it needs a "zero" in the compensation - normally provided by the ESR of that output capacitor. So putting a film or ceramic capacitor across the electrolytic (as so many audiophiles are fond of doing to make the caps "better") can be a serious mistake at the output side of a 3-terminal regulator. And Bob Pease would know, he designed many of the analog parts for National Semiconductor that have become long-lived standards in the industry, like the LM7800 series!