They gave us a paper where we have to correct the mistakes.

My twin cousins
I have identical twin cousins, Joe and John. They look exactly alike except that Joe has a tiny birthmark under his chin. Unless you look very closely,youd miss it. Both have straight, dark brown hair, but now Joes is longer because he wants to grow a ponytale.
The twins like many of the same things. They both play baseball and are on the Little League teams. Joe is a catcher and John is a second baseman. The twins also enjoy music, from jazz to rock to hip-hop. Joe plays the giuitar, and John plays the piano.
Theyre both good guys, but Joe is a bit more outgoing than John. John is specially shy in front of strangers. Joe, however, will casually saunter up to someone and say,"Hi. Im Joe." Joe is the one who would take a lead in the school play. John would rather work the lights or curtains. John told I he wants to be a doctor when he grows up. Joe prefers computers.

My corrections:

My Twin Cousins
I have identical twin cousins, Joe and John. They look exactly alike except that Joe has a tiny birthmark under his chin. Unless you look very closely, you'd miss it. Both have straight, dark brown hair, but now Joe's is longer because he wants to grow a ponytail.
The twins like many of the same things. They both play baseball and are on the Little League teams.Joe is a catcher and John is a second baseman. The twins also enjoy music, from jazz to rock to hip-hop. Joe plays the guitar and John plays the piano.
They're both good guys, but Joe is a bit more outgoing than John. John is especially shy in front of strangers. Joe, however, will casually saunter up to someone and say,"Hi, I'm Joe." Joe is the one who would take a lead in the school play. John would rather work the lights or curtains. John told me he wants to be a doctor when he grows up. Joe prefers computers.

Suggestions in caps.

My Twin Cousins

I have identical twin cousins, Joe and John. They look exactly alike (COMMA) except that Joe has a tiny birthmark under his chin. Unless you look very closely, you'd miss it. Both have straight, dark brown hair, but now Joe's is longer (COMMA) because he wants to grow a ponytail.

USE NEW PARAGRAPH TO INDICATE CHANGE OF IDEAS, PLACES, PERSONS OR TIMES.

The twins like many of the same things. They both play baseball and are on the Little League teams. (SPACE)Joe is a catcher (COMMA) and John is a second baseman. The twins also enjoy music, from jazz to rock to hip-hop. Joe plays the guitar (COMMA) and John plays the piano.

They're both good guys, but Joe is a bit more outgoing than John. John is especially shy in front of strangers. Joe, however, will casually saunter up to someone and say,"Hi, I'm Joe." Joe is the one who would take a lead in the school play. John would rather work the lights or curtains. John told me he wants to be a doctor (COMMA) when he grows up. Joe prefers computers.

REVIEW YOUR USE OF COMMAS.

http://grammar.ccc.commnet.edu/grammar/commas.htm

Great job on making the corrections! Here's a breakdown of the mistakes and how you fixed them:

1. "My twin cousins" should be capitalized to start the sentence correctly.
2. In the sentence "Unless you look very closely,youd miss it," there is a spacing error between "closely" and "you'd." It should be "closely, you'd."
3. In the sentence "Joe's is longer because he wants to grow a ponytale," "Joe's" should have an apostrophe to show possession, and "ponytale" should be corrected to "ponytail."
4. In the sentence "Joe plays the giuitar," "giuitar" should be corrected to "guitar."
5. In the sentence "Theyre both good guys," "Theyre" should be corrected to "They're" to indicate a contraction of "they are."
6. In the sentence "John told I he wants to be a doctor," "I" should be corrected to "me" to indicate the correct pronoun.

Overall, you made the necessary corrections to punctuation, capitalization, spacing, possessive forms, and contractions. Well done!