"How pacific do these errors have to be?"

Ha! It's supposed to be specific.

2a : restricted to a particular individual, situation, relation, or effect

Ex. a disease specific to horses

I agree with what cornbread ninja has written. The whole set of sentences uttered in the bottom drawings is marred with errors. To be correct, they should read :

"You're coughing up blood! I didn't know allergies could cause such a bad effect!" "Are there others like you? (It) Looks like it's getting worse." "How specific do these errors have to be?"

So the term you pointed out comes at the end of a long series of mistakes, thus contributing to the comic effect of the whole.

While I was writing my post, there was someone more rapid than me who commentated upon the same. Sorry if mine then seems to be a double.