One problem related to water pump has been reported for the 2012 Subaru Impreza. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2012 Subaru Impreza based on all problems reported for the 2012 Impreza.
Oil leak (small drip) from the front timing belt cover, on the driver side (side of the water pump). The leak is not obvious: due to the location, under the cover, it is not visible from casual inspection. The small drip is caught by the engine undercover and does not leave a mark on the floor. It takes time to notice it. The cover started to leak about a year ago (2016), if not earlier--Subaru failed to identify the leak during scheduled maintenance until last month -- which is quite surprising. The front cover is supposed to be sealed (no gasket). The seal is supposed to last for the design life of the engine. Based on google search, this seal issue is a well documented defect of the factory seal at the location of the screws. In some cases, the leak was fixed by removing the screws, adding sealant and putting back the screws (my cover also seems to leak at the screw location too). This fix suggest a manufacturing defect during installation of the cover: failure to add sealant to the screws or failure to add sufficient amount of sealant at the screw location. Subaru now recommends a front cover reseal ($650). This known issue should have been dealt with during the engine warranty period.