Geothermal does cause earthquakes - but small ones.
The big new geothermal plant at Hellisheiði east of Reykjavik has been associated with a sharp uptick in earthquake activity around Hengill and Hveragerði. The earthquakes are being triggered by the injection of water after it has been bled of steam back into the reservoir. The largest of the quakes registers about 3.8 and they come in swarms of hundreds if not thousands spread over days or weeks. 3.8 is a noticeable jolt, but not really dangerous to anyone unless they're in a particularly fragile house - certainly not a problem in Iceland. The problem diminishes with time as the injection wells are brought up to full pressure and the rock around them becomes equally pressurised.
There have been no effects on the water table at Hellisheiði, although if you do visit the power station (and it is beautiful), you can't help but notice that geothermal has one big downside - hydrogen sulfide. But if that is the worst problem - bring it on!
The second big geothermal plant near Reykjavik at Svartsengi is also being used as a demonstration plant for methanol production. CO2 which is brought up in the well water is being separated and reacted with hydrogen to produce 5 million litres of methanol which will be added to petrol which is the country's biggest import by far.
Geothermal in Britain is more difficult as our geothermal gradient is pitiful in comparison to Iceland and large parts of the US. However, it would be good to see some imagination in putting the resources of Devon, Cornwall and the Peak District to work in generating clean electricity.