Very interesting plane indeed, lost out to the Me-109 due to a number of factors; politics and its complex structure, which made it somewhat difficult to be produced fast.
The last factor was reason for Ernst Heinkel to develop the easier-to-build He-100.
In 1938 the Dutch air force was allowed to test a factory He-112B at Soesterberg AFB. Both Dutch test pilots were stunned by the performance of this aircraft, it was simply amazingly fast and very advanced for its time.
Diving with speeds over 600 kph and fireing 2 cannons + 2 machineguns was something completely new for the (quite experienced) Dutch test pilots, who found themselves being pushed to new limits.
Mind you, this aircraft had only the 650 hp Jumo engine, the export version would have the 1100 pk Daimler.
The Dutch airforce wanted to buy 18 of these planes but the ordering never materialized due to the personal vision of some halfwit politician, who happened to Minister of Defence. He's also the reason the Dutch airforce never got its modern fighters to replace the Fokker D.XXI; the Spitfire, Hurricane and the He-112B were the most serious candidates.
Picture of the He-112B at Soesterberg:
http://www.oudsoesterberg.nl/joomla/cpg153/displayimage.php?pid=1235&fullsize=1