If I understand correctly, you can use split
to separate the valid and invalid dates:
split(dataValues,is.na(as.Date(dataValues$value1,dateFormat)))
$`FALSE`
id value1
1 a1 10/3/2012
5 a6 1/2/2012
7 a8 2/4/2012
11 a12 2/5/2012
13 a14 5/8/2013
14 a15 2/5/2014
15 a16 6/9/2010
16 a17 5/4/2014
$`TRUE`
id value1
2 a2 13/4/2012
3 a4 <NA>
4 a5 0
6 a7 2/30/2013
8 a9 N/A
9 a10 No Data
10 a11 5-6-2012
12 a13 Not Applicable