Hi Zvonka,
 
Grammatically, there isn�t anything wrong with the sentence, but it isn�t very elegant. Part of the reason is that she showed:
 
1. that she was an excellent team player
2. anticipation
3  hard work
 
As you can see, those are quite different kinds of things and therefore are perhaps better separated.
 
Also,  �she showed hard work� sounds odd. Perhaps  �she showed evidence of hard work�?
 
 �Liabilities � is an odd word to use in this context. I think  �weaknesses� might be better? I�d also change  �projects� because it sounds too specific, but it depends on the original meaning.  �Anticipation� is a skill that I�d associate with sport ( �anticipating the ball�), rather than management. So if this is about management skills, I might change  �anticipation� to  �initiative�.
 
If I rewrote it, it would look like this:
 
Mary proved not only that she is an excellent team player, but she also showed great initiative  and evidence of hard work despite her weaknesses in other areas.
 
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