createGapFiller<- function(gaps=c(NA,'')){
    currentVal <- NA
        func <- function(y){
            if (y %in% gaps) {
                return(currentVal) 
            }        
            else {  
                currentVal <<- y
                    return(y)
            }
        }
    return (function(v){
            mapply(func,v)
            })
}

myGapFiller<- createGapFiller(gaps=c(NA,''))
csvWithGaps <- read.csv('mydata.csv')
csvWithoutGaps <- data.frame(lapply(as.list(csvWithGaps),myGapFiller))

> csvWithGaps
    Condition File Record Time
1     Control   44      1  1.3
2               NA      2  5.3
3               NA      3  6.7
4               NA      4  3.5
5               NA      5  3.7
6               NA      6  8.3
7  Experiment   46      1  5.7
8               NA      2  3.6
9               NA      3  8.6
10              NA      4  3.5
11              NA      5  6.6
12              NA      6  6.6
13              NA      7  0.0
> csvWithoutGaps
    Condition File Record Time
1     Control   44      1  1.3
2     Control   44      2  5.3
3     Control   44      3  6.7
4     Control   44      4  3.5
5     Control   44      5  3.7
6     Control   44      6  8.3
7  Experiment   46      1  5.7
8  Experiment   46      2  3.6
9  Experiment   46      3  8.6
10 Experiment   46      4  3.5
11 Experiment   46      5  6.6
12 Experiment   46      6  6.6
13 Experiment   46      7  0.0