I think that it's important for parents to realize that colleges are trying to accept students with the maturity to be able to live at home and run their own lives without parents having to do lots of things for them.
Before the Internet existed, there were good reasons for parents to call schools to check on things like whether applications were complete: Because of students' school hours and EC hours, many students would not have been able to contact school officials until the offices were closed.
Those days are long gone, however ,and students can use e-mail to check on things like their application and to make arrangements for visiting. Certainly parents can guide students through these experiences since usually these are the first time students have had to do things like that, and the students need help from the parents' credit cards. However, parents should not need to be the ones contacting the colleges.
The only time I can think of good reason for parents to contact the colleges would be if there are questions about financial aid. Many parents understandably do not want their kids to know the intricacies of the family finances, so often parents need to make the calls about financial aid questions and follow-ups.
When it comes to thank-you notes, I think that the students should be the ones responsible for that. While it's nice when parents like colleges and appreciate tours, etc., I think that the real customer is the student (this is true even though parents usually pay the bills) and the student should be responsible for sending the notes of appreciation.