"Do not bring Dom. pesos, as this may cause problems at the custom (for you beeing a tourist), because it's still illegal to export DR$!!!! "
Dominican pesos are be bought and sold world wide. They can be bought and sold for example at Newark, JFK, San Juan, and Miami airport cash exchanges.
"You can change your checks and cash anywhere on the roads with money changers, which do have an office (don't trust the wild ones without offices!)or to the official rate in any banks! "
In tourist areas, changing money won't be a problem but it is not always easy to cash travelers checks in general and changing any currency is not always easy outside the tourist areas. Try it after 9pm for example while traveling along Autopista Las Americas. In Santo Domingo, most banks won't change US Dollars.
"When leaving the country, you will need to pay the USD 10.- Airport tax, which for reasons I do not know, they still collect in the old fashion way - in cash! "
Some airlines include this in the price of the ticket. The departure fee was US$15 from La Romana because it includes a $5 airport facilities charge. I'm not sure if the new airport also charges that way. Departure tax can be paid in Dominican pesos (I've paid it that way myself from time to time).
See the straight scoop on money in the Dominican Republic at www.BocaChicaBeach.net/money.html or click on the link below.