If they are all 2000 or later try this:
x <- c("10/01/00", "10/01/00", "10/20/2000", "05/13/2000") # test data
xx <- as.Date(sub("/(..)$", "/20\\1", x)); xx
## [1] "10/01/2000" "10/01/2000" "10/20/2000" "05/13/2000"
If the objective is to take the most recent date then this will work whether or not the dates are all 2000 or later provided there is no date more than 100 years old. Assuming we have already run the above line if all the dates are in the future then the most recent date must be in the 1900s so repeat the sub but with 19 instead of 20 and take the max; otherwise, the max date must be 20xx so remvove the dates in the future and take the max of what is left:
if (all(xx > Sys.Date()) max(as.Date(sub("/(..)$", "/19\\1", x)))
else max( xx[xx <= Sys.Date()] )
Update Some improvements.