Anything wrong with "in the all rounds" in the following sentence? What does it mean?
Eventually, Sabrina Vega competed in the 2012 Olympic trials. She finished 10th in the all rounds.

Question

Answer

Yes, there is something wrong. 
Somebody has misheard, misunderstood or mistranscribed this sentence:

'She finished 10th in the all-around.'

Here's a definition of 'all-around.':

Definition: The term all-around simply means all of the different gymnastics apparatus.

All-around results would be the total of all four events in women's gymnastics and rhythmic gymnastics, or all six events in men's gymnastics.

Answer

"all rounds" may be a special term for her sport

or

she finished 10th after all the rounds, might be better