Would "私を見て突っ込む所はないか" translate to something like "Would you come take a closer look at me?"
I've done a lot of context searching for 突っ込む所 but I can't quite pin down a solid meaning on it.
Forget about the 9-11 reference; That is just the literal meaning of the word.
Here, we are talking Japanese comedy slangs. If you have not seen any Japanese two-person stand-up comedy, you probably should before reading this answer. You will understand the term much better that way than getting an explanation.
I recommend that J-learners learn these words in pairs. Knowing only one of them will not help you much in the real Japanese-speaking world, trust me.
If you are the ボケ, you will just keep on telling jokes in an uninhibited manner trying to make people laugh. You can be illogical, rude, ignorant --- anything. People do not expect sanity or normalcy from you in the first place.
The ツッコミ must do the opposite. He keeps correcting and pointing out the irrationalities presented by the ボケ.
Point is, you do not have to be a comedian for others to expect you to talk like one in present-day Japan. Among the young and not so young generations, this boke-tsukkomi-style of talking rules. It is like everyone knows which type s/he is and they usually stick to it.