What were some of the characteristics of the Nightingale that made it easier for the frog to use her for his selfish and mean motive?

You are correct in identifying the from as "mean."  He
turns out to be kind of a jerk in the poem.  I think that the nightingale suffered from
a fatal combination of trust and insecurity.  The irony is that the nightingale is truly
talented, yet she has not been made aware in her own life of her gifts.  Note the lines,
"Quite unused to such applause/ Sang till dawn without a pause."  These help to bring
out that the nightingale both possesses talent, and yet does not realize her own
greatness.  This causes her to succumb to the praise of others and bask in the glory, as
if it's the first time she has experienced it.  The fact that the nightingale responds
and continues to respond to praise indicates to us that she can be easily manipulated.
 Notice again that she asks the frog, who has little musical talent, if he liked her
song. Think about that:  The person who has talent goes to the person who doesn't have
any for advice.  This had to have led the frog presume that he holds the power in their
relationship.  No doubt the frog has understood this, and rather than outwardly suggest
that she leave, he veils his venom and poison with the guise of experience.  When he
"critiques" her performance, she is "Greatly flattered and impressed/
That a
critic of such note/Had discussed her art and throat."  In this, we can see that the
nightingale has ceded power to the frog, emboldening him to pursue on his quest to
eliminate the competition.  He continues to play on her weaknesses, calling her a
"beginner" and assuring her that he can make her a "winner."  These are obviously
sensitive points for the nightingale who takes the bait, in all of its forms.  When we
see her, "flushed with confidence," it's the beginning of the end.  The frog has her and
does everything in his power to ruin her voice under the pretense of "training."  This
is because he is indeed mean, but because the nightingale allowed herself to be used and
abused.  If she had the confidence to either sing her song and care not for the frog, or
to rebuke the frog's attempts, or even not care in what he says, she would have been
better off and would not have been run off and lost her precious talent.  In the end,
the sadness of the nightingale and the cruelty of the frog make a bitter combination for
her and a great one for him.

Makes you dislike
frogs, eh?