I ran a quick correlation for each position containing the players qualified according to PMR - those who were on the field for at least 1000 balls in play.
There were definitely some issues in center field, and to a lesser extent 2B. The two systems had a high level of agreement in the corner OF positions.
The 10 biggest disagreements were:
Both PMR and UZR were calculated using the Baseball Info Solutions (BIS) data set this season. I wonder if David or MGL might be able to give some ideas as to where the differences might come from.