In Noble Eightfold Path, Right Mindfulness is a factor in the path. This implies that there are Wrong Mindfulness, things you shouldn't be mindful of.
Consider:
The definition (the four frames of reference)
"And what is right mindfulness? There is the case where a monk remains
focused on the body in & of itself — ardent, alert, & mindful —
putting aside greed & distress with reference to the world. He remains
focused on feelings in & of themselves... the mind in & of itself...
mental qualities in & of themselves — ardent, alert, & mindful —
putting aside greed & distress with reference to the world. This is
called right mindfulness...
"This is the direct path for the purification of beings, for the
overcoming of sorrow & lamentation, for the disappearance of pain &
distress, for the attainment of the right method, & for the
realization of Unbinding — in other words, the four frames of
reference."
— DN 22
As well as:
Abandoning the wrong factors of the path
"One is mindful to abandon wrong view & to enter & remain in right
view: This is one's right mindfulness...
"One is mindful to abandon wrong resolve & to enter & remain in right
resolve: This is one's right mindfulness...
"One is mindful to abandon wrong speech & to enter & remain in right
speech: This is one's right mindfulness...
"One is mindful to abandon wrong action & to enter & remain in right
action: This is one's right mindfulness...
"One is mindful to abandon wrong livelihood & to enter & remain in
right livelihood: This is one's right mindfulness..."
— MN 117
http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-sati/
Essentially you need to be mindful of Right View, Right Intention, Right Speech, Right Action and Right Livelihood, if you are not mindful of those things you are not practicing Right Mindfulness. If you are mindful of wrong views and wrong intentions for example, it is also not Right Mindfulness.