You're right that somehow pre-war Wehrmacht has got a reputation as being something they were very much not - efficient and high tech. It was only 80% of German artillery that was horse drawn or more accurately only partially motorised at the outbreak of war. German infantry was entirely on foot (and frequently commandeered or stole bicycles). More importantly, Wehrmacht supply and logistics were woefully lacking mechanisation. The highly mechanised blitzkrieg was certainly partially PR, but was also a reaction the fact that the army was so poorly equipped in 39. They focused mechanisation on achieving full mechanisation rather than spreading it "fairly" across regiments. The had a small number of completely mechanised regiments, with fully modern equipment, and "the rest".

Still, you can't escape the fact blitzkrieg was also effective. It was effective as tactics had not evolved far from WW1 trench warfare. It was but a very small part of the military whole.

There were lots of shortcomings in the German war machine - for example, they never developed a successful 4 engine bomber severely limiting the bomb loads they could send, and range.

As to holocaust, my UK history lessons, before this mini series was made, and books referred to "the holocaust" as the main term, occasionally referring to the Nazi term "the final solution".