The OP asks for comments from university-level professors on whether (a) they have seen a decreasing trend in arithmetic skills among their students over time, and whether (b) such a trend might be attributable to the use of calculators. 1973 was roughly the last year in which one could teach freshman calculus to a group of students who had not been exposed to electronic calculators. Anyone who was teaching freshman calc in 1973 is at least ~64 years old, so at most we will have a very thin cohort of teachers who can comment on how their own students in 2012 compare to their past students who used slide rules.
It's also very risky to use anecdotal or subjective evidence to measure such trends. The best objective evidence that I'm aware of is in a book called Academically Adrift, Arum and Roksa, 2011. The authors document that certain downward trends have indeed occurred over the last 50 years. Two such trends are a marked decrease in the time students spend studying and a decrease in the amount of improvement in critical thinking and writing skills that occurs while students are in college. These trends persist even when one controls for such factors as the greater percentage of the population that now attends college.
I teach have been teaching physics at a community college in California since 1996. In my experience the main difference between students who have taken a calculus course and those who haven't is an increased probability that they will be fluent in basic arithmetic and algebra (e.g., being able to solve a=b/c for the variable c). This may indicate that they can't pass calculus with a C without these skills, or it may be an example of self-selection.
I find that very few students who have passed calculus can do any of the following without extensive coaching and remediation: Differentiate or integrate any function that is expressed in terms of variables other than x and y. Differentiate or integrate an expression containing symbolic constants. State the geometrical interpretations of the integral and derivative. Find the value of $x$ that maximizes $-x^2+x-2$. State under what circumstances $\Delta y/\Delta x$ is a valid measure of a rate of change, and under what circumstances $dy/dx$ is needed instead. Determine whether a car's odometer performs differentiation, or integration.
In other words, if we label the courses in a college-level math sequence with successive integers, what I find is that students who have passed course $n$ can only be counted on to display some level of competence in the material covered in course $n-3$ or $n-4$.
