If I roll Mr. Monopoly on the speed die, and all the properties have been bought, according to the rules I have to move to the next place that I have to pay rent. I am not clear what is the rule if the next place is the Auction which according to the rules makes me move to the place with the highest rent. Do I have to move to Auction or do I move to the next property which has cheaper rent.
The latter (you move to the next property which has cheaper rent.). It's not the next "place" in the rule, it's the next property .
From The Rules
If you roll a Mr. Monopoly after all of the properties are owned, make a normal move according to the white dice, then move ahead to the first property on which you need to pay rent