you should use ddply from plyr and split on all of the columns if you want to take into account the different reasons, if you want to ignore them don't use those columns in the split. You'll need to clean up some of the question marks and extra stuff first though.
x <- ddply(data, c("split_column1", "split_column3" etc),
summarize(result_df, stats you want from result_df))
Make it "long":
library(reshape)
dnow <- read.csv("~/Downloads/catsample20100504.csv")
dnow <- melt(dnow, id.vars=c("Student", "instructor"))
dnow$variable <- NULL ## since ordering does not matter
subset(dnow, Student%in%c(41,42)) ## see the results
What to do next will depend on the kind of analysis you would like to do. But the long format is the useful for irregular data such as yours.
What's the (bigger picture) question you're attempting to answer? Why is this information interesting to you?
Are you just trying to find patterns such as 'if the student does this, then they also likely do this'?
Something I'd consider if that's the case - split the data set into smaller random samples for your analysis to reduce the risk of false positives.
Interesting problem though!